What is the factored form of the polynomial? x2 + 9x +20?
Summary: The factored form of the polynomial x2 + 9x + 20 is (x + 5)(x + 4).
x2−9x+20=(x2−5x)+(−4x+20)=x(x−5)−4(x−5)=(x−4)(x−5).
The roots of the equation x2−9x+20=0 are 4,5.
The factored form of a polynomial means it is written as a product of its factors. The factors are also polynomials, usually of lower degree.
A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value. To solve an equation is to find the solution(s) for that equation.
A solution to an equation is a number that can be plugged in for the variable to make a true number statement. 3(2)+5=11 , which says 6+5=11 ; that's true! So 2 is a solution.
Answer and Explanation: We are given the equation x 2 + 9 x = 6 . Therefore, the solutions of the given equation are x = − 9 + 105 2 , x = − 9 − 105 2 .
The only pair of factors of 16 that add up to -6 are 2 and -8, so these are the numbers we will use to fill in the blanks. That is, x2 - 6x - 16 = (x + 2)(x - 8).
Given, the polynomial is x² + 9x + 18. We have to factorise the polynomial. Therefore, the factors are (x + 3) and (x + 6).
When the quadratic expression is a product of two factors where each one is a linear expression, this is called the factored form. An expression in factored form can be rewritten in standard form by expanding it, which means multiplying out the factors.
What is an example of a factored form?
An example for a quadratic function in factored form is y=½(x-6)(x+2). We can analyze this form to find the x-intercepts of the graph, as well as find the vertex.
Factored form helps us identify the x-intercepts or zeros of the function.
An expression is in factored form only if the entire expression is an indicated product. Factoring is a process that changes a sum or difference of terms to a product of factors. A prime expression cannot be factored.
- Move all terms to one side of the equation, usually the left, using addition or subtraction.
- Factor the equation completely.
- Set each factor equal to zero, and solve.
- List each solution from Step 3 as a solution to the original equation.
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In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
- Mathway.
- Photomath.
- Microsoft Math Solver.
- Cymath.
- QuickMath.
- Symbolab.
- Chegg Math Solver.
For decades, a math puzzle has stumped the smartest mathematicians in the world. x3+y3+z3=k, with k being all the numbers from one to 100, is a Diophantine equation that's sometimes known as "summing of three cubes."
What are the solutions of x2 = -5x + 8? Summary: The solutions that satisfies the equation x2 = -5 x + 8 are (-5 - √57) / 2 and (-5 + √57) / 2.
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations.
How do you solve quadratic equations with solutions?
- Write the quadratic equation in standard form, ax2 + bx + c = 0. Identify the values of a, b, and c.
- Write the Quadratic Formula. Then substitute in the values of a, b, and c.
- Simplify.
- Check the solutions.
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.
So, x2+2x−15=(x−3)(x+5)
Hence, x2−4x−21=(x−7)(x+3)
∴x2+7x−18=(x−2)(x+9) Was this answer helpful?
∴ The factors of x2+6x+9 are (x+3) and (x+3).
Hence, factorisation of 9x2 – 3x – 20 is 3 x - 5 3 x + 4 .
∴ The factor of x2 - 9x + 18 is (x - 6) and (x - 3).
The only options are -5 and 2, therefore 3x^2 - 9x - 30 = 3(x-5)(x+2).
Hence, the factors of 9 x 2 + 18 x + 8 are ( 3 x + 4 ) ( 3 x + 2 ) .
What is the factored form of the following expression 9x2 30x 25?
Therefore, factors of 9x2+30x+25 are (3x+5)(3x+5)
Hence, x2+9x−22=(x−2)(x+11).
The factors of the equation x2 - 9x + 14 are (x - 2) (x - 7) which satisfies the equation.
Therefore, the factors of x2+6x+9 are (x+3)(x+3).
Hence factors of x2+6x+8 are (x+4)(x+2)
References
- https://www.cnn.com/cnn-underscored/money/historical-mortgage-rates
- https://www.stlouisfed.org/on-the-economy/2017/january/why-federal-reserve-regulate-banks
- https://byjus.com/question-answer/solve-the-quadratic-equation-x-2-9x-20-0-45-5-1-51-23-1/
- https://www.bankrate.com/home-equity/do-i-lose-home-equity-after-refinancing/
- https://www.investopedia.com/articles/active-trading/053115/average-rate-return-day-traders.asp
- https://www.cfr.org/backgrounder/what-us-federal-reserve
- https://www.linkedin.com/pulse/why-do-most-retail-traders-90-lose-money-how-can-more
- https://www.t4trade.com/en/what-is-the-hardest-part-of-trading/
- https://www.bankrate.com/mortgages/pros-and-cons-15-year-mortgage/
- https://www.toppr.com/ask/en-qa/question/factorise-x2-6x-8/
- https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:factored-form-quadratics/v/graphing-quadratics-in-factored-form
- https://study.com/academy/lesson/warren-buffet-biography-education-quotes.html
- https://www.cuemath.com/questions/which-is-a-factor-of-x2-9x-14/
- https://study.com/academy/lesson/how-to-solve-x-2-6x-16.html
- https://stockanalysis.com/article/warren-buffett-money/
- https://www.quora.com/Is-it-possible-to-earn-1-000-daily-through-day-trading-or-stock-market-investments
- https://www.toppr.com/ask/question/factorise-the-following-polynomial-9x230x25/
- https://pictureperfectportfolios.com/how-warren-buffetts-mentors-shaped-his-investment-philosophy/
- https://www.forex.com/ie/news-and-analysis/how-to-use-the-5-3-1-trading-strategy-in-forex/
- https://www.chegg.com/homework-help/questions-and-answers/two-government-policies-favor-businesses-q159073154
- https://www.nerdwallet.com/mortgages/mortgage-rates/30-year-fixed
- https://www.tradersmastermind.com/a-look-at-the-best-ever-trades-in-history/
- https://finance.yahoo.com/news/dont-pass-math-homebuyers-call-130700730.html
- https://www.zoopla.co.uk/discover/property-news/will-mortgage-rates-go-down/
- https://www.unit21.ai/fraud-aml-dictionary/regulatory-agencies
- https://www.investopedia.com/ask/answers/040915/what-demandside-economics.asp
- https://markets.businessinsider.com/news/stocks/warren-buffett-berkshire-hathaway-annual-salary-compensation-40-years-2021-3-1030229588
- https://byjus.com/question-answer/which-of-the-following-is-a-factor-of-x-2-6x-9-8-x-x-1/
- https://www.ziprecruiter.com/Salaries/Retail-Trader-Salary
- https://im.kendallhunt.com/HS/students/1/6/9/index.html
- https://www.mstock.com/articles/5-reasons-why-traders-lose-money-in-stock-market
- https://www.toppr.com/ask/question/factorize-the-following-using-the-identitiesx2-6x-9/
- https://www.investopedia.com/will-2024-mortgage-rates-fall-clues-from-wednesdays-fed-announcement-8611482
- https://www.minneapolisfed.org/article/2006/types-of-enforcement-actions
- https://www.toppr.com/ask/question/factorisex2-7x-18/
- https://www.federalreserve.gov/aboutthefed/the-fed-explained.htm
- https://study.com/academy/lesson/types-of-regulation-privatization-deregulation.html
- https://www.federalreserve.gov/aboutthefed/files/pf_5.pdf
- https://turbotax.intuit.com/tax-tips/investments-and-taxes/day-trading-taxes-what-new-investors-should-consider/L9ToKa1qo
- https://www.rocketmortgage.com/learn/average-mortgage-length
- https://brightlinkprep.com/best-calculators-for-college-algebra/
- https://money.usnews.com/loans/mortgages/mortgage-rate-forecast
- https://tradethatswing.com/the-real-reasons-most-traders-lose-money-day-trading-or-swing-trading/
- https://www.lendingtree.com/home/refinance/how-soon-can-i-refinance-my-mortgage/
- http://dl.uncw.edu/digilib/Mathematics/Algebra/mat111hb/PandR/quadratic/quadratic.html
- https://www.varsitytutors.com/hotmath/hotmath_help/topics/solving-equations
- https://www.splashlearn.com/math-vocabulary/number-sense/equation
- https://www.fdic.gov/resources/consumers/other-regulators.html
- https://resourcehub.bakermckenzie.com/en/resources/global-financial-services-regulatory-guide/north-america/united-states-of-america/topics/who-regulates-banking-and-financial-services-in-your-jurisdiction
- https://www.mytutor.co.uk/answers/31100/GCSE/Maths/Factorise-3x-2-9x-30/
- https://resume.co/blog/highest-paying-trade-jobs
- https://www.axiory.com/trading-resources/basics/best-stock-traders-ever
- https://www.cnbc.com/2020/08/30/how-warren-buffett-made-billions-became-oracle-of-omaha.html
- https://www.netnethunter.com/does-warren-buffett-drive-his-own-car
- https://www.wyzant.com/resources/lessons/math/algebra/solve-factoring/
- https://gitnux.org/day-trading-statistics/
- https://www.cabotwealth.com/daily/value-stocks/benjamin-graham-a-short-biography
- https://www.wellsfargo.com/financial-education/homeownership/loan-amortization-extra-payments/
- https://www.educationise.com/post/8-free-math-problem-solving-websites-and-applications
- https://www.businessinsider.com/how-warren-buffett-spends-money-net-worth
- https://www.cbsnews.com/news/warren-buffett-donates-870-million-to-charities-before-thanksgiving/
- https://www.investopedia.com/terms/b/bengraham.asp
- https://byjus.com/maths/quadratics/
- https://www.linkedin.com/pulse/why-traders-fail-3-major-failure-points-avoid-mfta-cmt-cfte-msta-z9mbc
- https://www.brookings.edu/articles/we-must-focus-on-bank-supervision/
- https://byjus.com/question-answer/factorize-the-following-algebraic-expression-x-2-4x-21-1/
- https://www.finra.org/investors/investing/investment-products/stocks/day-trading
- https://www.linkedin.com/pulse/what-90-rule-forex-broker-forex-global-czp0c
- https://www.warriortrading.com/how-to-make-a-living-day-trading/
- https://money.usnews.com/loans/mortgages/articles/historical-mortgage-rates
- https://www.money.co.uk/mortgages/should-you-get-a-long-or-short-term-mortgage
- https://www.cmcmarkets.com/en/trading-guides/top-3-trading-mistakes-and-how-to-avoid-them
- https://www.cbsnews.com/news/whats-the-best-way-to-get-a-lower-mortgage-rate-experts-weigh-in/
- https://www.collegeconsensus.com/degrees/stockbroker/
- https://www.cnbc.com/2017/09/29/warren-buffett-credits-his-success-to-these-3-people.html
- https://smallbusinessbc.ca/article/three-famous-billionaire-entrepreneurs-and-their-mentors/
- https://www.pennfoster.edu/blog/in-demand-skilled-trades-jobs
- https://pressbooks.bccampus.ca/algebraintermediate/chapter/solve-quadratic-equations-using-the-quadratic-formula/
- https://www.kundankishore.in/blog/is-it-possible-to-become-rich-by-stock-trading-do-people-make-enough-out-of-day-trading
- https://dfpi.ca.gov/consumers-who-regulates-a-financial-institution/
- https://poe.com/poeknowledge/1512928000358234
- https://www.moneycontrol.com/news/trends/warren-buffetts-wife-overhead-complaining-about-rs-300-coffee-at-billionaires-summer-camp-10967151.html
- https://www.investopedia.com/articles/personal-finance/042015/pros-and-cons-15year-mortgage.asp
- https://www.investopedia.com/terms/p/pumpanddump.asp
- https://www.bankrate.com/mortgages/30-year-mortgage-rates/
- https://www.reed.co.uk/courses/career-guides/how-to-become-a-day-trader
- https://www.investopedia.com/ask/answers/042115/what-caused-stock-market-crash-1929-preceded-great-depression.asp
- https://market-bulls.com/richest-traders/
- https://www.investopedia.com/terms/f/fiftypercentprinciple.asp
- https://homework.study.com/explanation/why-does-it-take-30-years-to-pay-off-a-150-000-loan-even-though-you-pay-1-000-a-month.html
- https://www.debt.org/real-estate/mortgages/15-year-fixed/
- https://finance.yahoo.com/news/warren-buffett-says-dies-90-133400915.html
- https://www.dukascopy.com/swiss/english/marketwatch/articles/top-10-most-successful-forex-traders-in-the-world/
- https://www.usa.gov/branches-of-government
- https://www.theinvestorspodcast.com/warren-buffett-investment-strategy/module-2/warren-buffetts-4-rules/
- https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Arithmetic_and_Algebra_(ElHitti_Bonanome_Carley_Tradler_and_Zhou)/01%3A_Chapters/1.17%3A_Equations_and_their_Solutions
- https://byjus.com/question-answer/9x2-18x-8-factorise-it/
- https://portal.ct.gov/DOB/Consumer/Consumer-Education/ABCs-of-Banking---Banks-and-their-Regulators
- https://www.occ.treas.gov/about/index-about.html
- https://www.rbi.org.in/commonperson/English/scripts/preface.aspx
- https://craftjack.com/toolbox/toughest-contractor-jobs
- https://www.centralbank.ie/consumer-hub/explainers/what-is-financial-regulation-and-why-does-it-matter
- https://www.investopedia.com/articles/trading/09/risk-management.asp
- https://www.quantifiedstrategies.com/what-percentage-of-day-traders-fail/
- https://quickmath.com/webMathematica3/quickmath/algebra/factor/basic.jsp
- https://en.wikipedia.org/wiki/Warren_Buffett
- https://finance.yahoo.com/news/warren-buffett-accumulated-99-net-193522940.html
- https://www.forbes.com/sites/bill_stone/2024/03/03/three-timeless-investment-lessons-from-warren-buffetts-annual-letter/
- https://www.investopedia.com/articles/01/071801.asp
- https://www.bankrate.com/banking/what-to-expect-from-your-failed-bank/
- https://www.toppr.com/ask/en-us/question/factorise-x22x15/
- https://www.investopedia.com/terms/d/daytrader.asp
- https://www.americanfinancing.net/saving-money/extra-mortgage-principal-payments
- https://byjus.com/question-answer/factorise-9x2-3x-20/
- https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-forms-features/v/interpret-quadratic-models-factored-form
- https://www.bosshunting.com.au/hustle/warren-buffett-iq-succeed/
- https://www.cuemath.com/questions/what-is-the-factored-form-of-the-polynomial-x2-9x-20/
- https://www.yondu.com/articles/7-banking-regulations-in-the-philippines-a-digestible-review
- https://www.toppr.com/ask/question/factorize-the-followingx2-9x-22/
- https://testbook.com/question-answer/factorize-x2-9x-18--60533152e463ed0804203fe9
- https://www.ck12.org/book/CK-12-Algebra-Basic/section/9.4/
- https://www.imf.org/en/Publications/fandd/issues/Series/Back-to-Basics/Fiscal-Policy
- https://ftmo.com/en/day-trading-for-a-living/
- https://www.investopedia.com/mortgage/refinance/when-and-when-not-to-refinance-mortgage/
- https://tradethatswing.com/the-day-trading-success-rate-the-real-answer-and-statistics/
- https://www.popularmechanics.com/science/math/a28943849/unsolvable-math-problem/
- https://www.homeloanexperts.com.au/home-loan-articles/retirement-age-home-loan/
- https://en.wikipedia.org/wiki/Regulation
- https://www.fool.com/investing/how-to-invest/stocks/day-trading/
- https://www.linkedin.com/pulse/read-why-most-traders-quit-timon-rossolimos
- https://www.linkedin.com/pulse/what-type-trading-should-beginner-start-prince-john-paul-rpige
- https://www.ramseysolutions.com/retirement/what-is-day-trading
- https://www.vrdnation.com/how-long-does-it-take-to-learn-trading/
- https://bullishbears.com/how-much-do-day-traders-make/
- https://www.cuemath.com/ncert-solutions/factorise-x2-plus-9x-plus-18/
- https://www.rocketmortgage.com/learn/15-vs-30-year-mortgage
- https://bullishbears.com/retail-traders/
- https://www.stlouisfed.org/in-plain-english/introduction-to-supervision-and-regulation
- https://www.toppr.com/ask/question/factorise-x2-9x-20/
- https://www.nasdaq.com/articles/two-ways-warren-buffetts-protege-handles-investments-differently-than-him
- https://www.investopedia.com/ask/answers/063015/what-are-some-major-regulatory-agencies-responsible-overseeing-financial-institutions-us.asp
- https://www.atlanticbay.com/knowledge-center/pros-and-cons-of-a-30-year-fixed-rate-mortgage/
- https://www.cuemath.com/questions/which-are-the-solutions-of-x2-5x-8/
- https://www.glassdoor.com/Salaries/day-trader-salary-SRCH_KO0,10.htm
- https://homework.study.com/explanation/what-are-the-solutions-of-x-2-plus-9x-6.html
- https://www.newtraderu.com/2023/10/17/warren-buffett-i-read-5-6-hours-a-day/
- https://medium.com/@Levente22/shocking-but-true-90-of-people-lose-money-in-stocks-9da95870cbe8
- https://www.indeed.com/career-advice/finding-a-job/trading-degree
- https://www.military.com/veteran-jobs/4-life-lessons-warren-buffett-learned-his-military-service.html
- https://buffett.cnbc.com/about-buffett/
- https://www.bankrate.com/mortgages/mortgage-interest-rates-forecast/
