Polynomial Division by Factoring
Read this topicExplanations 4
- There are many different methods for dividing polynomials, but one thing remains the same: every division will have a divisor (the denominator of the fraction) and the dividend …
By Stefan Cuevas, Joshua Siktar, Evan Fang, Victor Wang, Alex Federspiel, Amy Feraco, Vatsal Ojha, Anusha Rahman
- (Video) Divide a Polynomial by a Monomial by YourMathGal The above video is from the YouTube channel YourMathGal, in which she describs how to divide polynomials in the case whe…
By Stefan Cuevas, Alex Federspiel, Joshua Siktar, Amy Feraco
- Dividing Polynomials When you're dividing a polynomial by another term (whether it's a monomial, a binomial, a trinomial, or another polynomial), the key things to remember are …
By Hannah Bonville, Alex Federspiel, Eunji Kwon, Joshua Siktar, Evan Fang, Anusha Rahman
- Polynomial Division by Factoring Welcome to the first lesson on polynomial division! In this lesson, we will explore how to divide polynomials using factoring, a method that sim…
By Trisha, Anusha Rahman
Problems 26
- What is the maximum value of 3x2+9x+173x2+9x+7\frac{3x^2+9x+17}{3x^2+9x+7}3x2+9x+73x2+9x+17 over all real numbers x?x?x? Source: ARML 1986
- Which of the following is not a polynomial?
- For how many distinct integers nnn is x3+4x2+4xx^3 + 4x^2 + 4xx3+4x2+4x divisible by x+nx+nx+n?
- Simplify x2+6x+9x+3\frac{x^2+6x+9}{x+3}x+3x2+6x+9 if x+3≠0x+3\neq0x+3=0.
- Express 7x2−71−x2\frac{7x^2-7}{1-x^2}1−x27x2−7 in its simplest form, assuming x2≠1x^2\neq 1x2=1.
- Simplify the fraction 64z9x740z4x2\frac{64z^9x^7}{40z^4x^2}40z4x264z9x7 if xxx and zzz are nonzero.
- Simplify 12x2−24x−618.\frac{12x^2-24x-6}{18}.1812x2−24x−6.
- What is another way to write the expression 9x2+15x−33x\frac{9x^2+15x-3}{3x}3x9x2+15x−3 if x≠0x\neq0x=0?
- Simplify 3x2−6x−45x−5\frac{3x^2-6x-45}{x-5}x−53x2−6x−45 assuming x≠5x\neq5x=5.
- If xxx and yyy are nonzero variables, then −10x7y3+22x8y2−14xy102x3y5\frac{-10x^7y^3+22x^8y^2-14xy^{10}}{2x^3y^5}2x3y5−10x7y3+22x8y2−14xy10 is equivalent to which expression be…
- Simplify the expression 2x2−6x+4x−1\frac{2x^2-6x+4}{x-1}x−12x2−6x+4 assuming the denominator is nonzero.
- The total number of visitors who came to the Washington Theatre from May 1 to May 31 can be modeled by the function F(x)=126x3+279x2+90x+450F(x)=126x^3+279x^2+90x+450F(x)=126x3+…
- Simplify 7x2−21x−70x−5\frac{7x^2-21x-70}{x-5}x−57x2−21x−70 assuming x−5≠0x-5\neq0x−5=0.
- Factor the numerator of the fraction 7x2+21x−280x−5\frac{7x^2+21x-280}{x-5}x−57x2+21x−280 as written, without simplifying.
- Simplify 49x4+140x2+100(7x2+10)2\frac{49x^4+140x^2+100}{(7x^2+10)^2}(7x2+10)249x4+140x2+100
- Simplify 36x3−16x2+4x4x\frac{36x^3-16x^2+4x}{4x}4x36x3−16x2+4x if xxx is nonzero.
- Using the information above, determine the average price per gallon of gas in 2012.
- Can we factor the numerator of 3x2−3x−18x−3\frac{3x^2-3x-18}{x-3}x−33x2−3x−18 before dividing?
- Rewrite ab+xc.\frac{ab+x}{c}.cab+x.
- Select the easiest method for the division problem x3+6x+8x3+6x.\frac{x^3+6x+8}{x^3+6x}.x3+6xx3+6x+8.
- Simplify 8x3y−4x2y22x2y\frac{8x^3y-4x^2y^2}{2x^2y}2x2y8x3y−4x2y2 by canceling factors.
- Find the remainder when (2x3+3)(x−1)+π(\sqrt{2} x^3 + \sqrt{3})(x-1) + \pi(2x3+3)(x−1)+π is divided by x−1x - 1x−1. (Hint: Can you find the quotient without doing any work?)
- Select all expressions equivalent to 2x2+3x32x4\frac{2x^2+3x^3}{2x^4}2x42x2+3x3 for nonzero values of xxx.
- Find the largest integer nnn such that n−2016n-2016n−2016 divides n2−2016n^2-2016n2−2016. Source: Lexington Math Tournament.
- Simplify: x2−7x−11x−8\frac{x^2 - 7x -11}{x-8}x−8x2−7x−11
- Simplify: 2x2−17x−382x+3\frac{2x^2 - 17x - 38}{2x + 3}2x+32x2−17x−38