Factor by Grouping - Definition & Examples
Read this topicExplanations 5
- A common factor is a term or expression that divides evenly into all of a polynomial's terms. For example, the polynomial ab+acab + acab+ac has a common factor of aaa. Now, when…
By Vinitha Ranganeni, Naomi Burgess, Alex Federspiel
- (Videos) Factoring Trinomials: Grouping and Trial and Error by PatrickJMT These videos by Patrick JMT show how to factor by grouping. Summary\large{\text{Summary}}Summary The gr…
By Ben Ferrara, Naomi Burgess, Alex Federspiel, Amy Feraco, Jonathan Heller, Anusha Rahman
- What If We Don't Have a GCF? Remember that the acronym GCF stands for greatest common factor. It is the largest possible term that can divide evenly into each term of an express…
By Hannah Bonville, Naomi Burgess, Alex Federspiel, Amy Feraco, Jonathan Heller, Anusha Rahman
- (Video) Factoring by Grouping by mathman1024 This video by mathman1024 demonstrates the factor by grouping method. Summary\large{\text{Summary}}Summary The first polynomial our …
By Alex Federspiel, Naomi Burgess, Liza Sulkin, Amy Feraco, Jonathan Heller, Anusha Rahman
- Grouping Cubics We can break a polynomial into smaller groups with a common factor. This method is especially helpful when factoring cubic functions. This is called factoring by…
By Joshua Siktar, Jonathan Heller, Anusha Rahman, Caroline K
Problems 32
- x3−xx^3-xx3−x has which of the following factors?
- Factor by grouping: 16x3+4x2−4x−116x^3 + 4x^2 - 4x - 116x3+4x2−4x−1
- Factor the following cubic polynomial: 81x3+9x2−9x−181x^3 + 9x^2 -9x-181x3+9x2−9x−1.
- A rectangular prism has a volume given by 2x3−3x2−2x+32x^3 - 3x^2-2x+32x3−3x2−2x+3. Which of the following choices gives a possible length, width, and height of this rectangular…
- Divide x3−x2−xy+yx^3 - x^2 - xy + yx3−x2−xy+y by x2−yx^2-yx2−y.
- Factor and use the zero product property to find the solution(s) to the equation: 0=x3−4x0=x^3-4x0=x3−4x
- For how many integers nnn is x+nx+nx+n a factor of the polynomial x3+10x2+2xx^3 + 10x^2 + 2xx3+10x2+2x?
- How many factors of the form 4x+n4x+n4x+n (where nnn is an integer) does the polynomial 80x3−16x2−5x+180x^3 - 16x^2 -5x + 180x3−16x2−5x+1 have?
- The polynomial 2x3+4x2+5x+102x^3 + 4x^2 + 5x + 102x3+4x2+5x+10 has a linear factor. What is it?
- For how many integers nnn is x+nx+nx+n a factor of 16x3−16x2−32x16x^3 - 16x^2 - 32x16x3−16x2−32x?
- A cylinder has a volume of πx3+2πx2+πx\pi x^3 + 2\pi x^2 + \pi xπx3+2πx2+πx. Which of the following choices gives a possible radius and height of the cylinder, in terms of xxx? …
- Find the solutions to the quadratic equation: (x−3)(x−2)+(x−3)(x−6)=0(x-3)(x-2) + (x-3)(x-6) = 0(x−3)(x−2)+(x−3)(x−6)=0
- How many real roots does x3+x2=−x−1x^3+x^2 = -x-1x3+x2=−x−1 have?
- Jared wants to make a box. The possible heights xxx of the box satisfy the equation x3−4x2−x+4=0x^3-4x^2-x+4 = 0x3−4x2−x+4=0. Select the heights that the box can be.
- Express the number of trees that need to be planted in terms of area used.
- For how many integers nnn is x+nx+nx+n a factor of 4x3+4x2+x4x^3 + 4x^2 + x4x3+4x2+x?
- For how many distinct integers nnn is x3+4x2+4xx^3 + 4x^2 + 4xx3+4x2+4x divisible by x+nx+nx+n?
- Which of the following is not a step in factoring x2−2x+4x−8x^2 - 2x + 4x - 8x2−2x+4x−8 by grouping the first two and last two terms?
- Factor by grouping: 3x3+9x2−2x−63x^3 + 9x^2 - 2x - 63x3+9x2−2x−6
- Factor x2−x+21x−21x^2-x + 21x-21x2−x+21x−21.
- Factor xy+3x+4y+12xy+3x+4y+12xy+3x+4y+12.
- Factor x3−x2+x2−x+x−1x^3-x^2 + x^2-x + x-1x3−x2+x2−x+x−1.
- Find a constant ccc such that the cubic polynomial x3+2x2+cx+16x^3 + 2x^2 + cx + 16x3+2x2+cx+16 has x+2x+2x+2 as a factor.
- Is x2−xy+21xy−21y2x^2-xy + 21xy-21y^2x2−xy+21xy−21y2 divisible by x−yx-yx−y? If so, find the quotient.
- Find a value of aaa such that 2x3−4x2+ax−142x^3 - 4x^2+ax-142x3−4x2+ax−14 has a factor of 2x2+72x^2+72x2+7 in it.
- How many solutions does the following equation have? 3x3+3x2−4x−4=−8x−8\begin{align*} 3x^3 + 3x^2 - 4x - 4 = -8x-8 \end{align*}3x3+3x2−4x−4=−8x−8
- What value of ccc would make the following equation have a factor of x−2x-2x−2 in it? x3−cx2−5x+10\begin{align*} x^3-cx^2-5x+10 \end{align*}x3−cx2−5x+10
- How many solutions does the following equation have? x4+7x3+3x2+21x=0\begin{align*} x^4 + 7x^3 + 3x^2 + 21x = 0 \end{align*}x4+7x3+3x2+21x=0 (This is more than a cubic but see …
- How many solutions does the following equation have? x3−2x2−4x+8=0x^3-2x^2-4x+8 = 0x3−2x2−4x+8=0
- Factor the following polynomial: x3−4x2+3x−12x^3 - 4x^2 + 3x -12x3−4x2+3x−12
- Factor the following polynomial by grouping: x3−3x2+6x−18x^3 - 3x^2 + 6x - 18x3−3x2+6x−18
- Find the number of ordered pairs of positive integers (x,y)(x,y)(x,y) such that x+y≤2019x+y \le 2019x+y≤2019 and the rational expression x3−x2y+2x+xy2−y3−2y+1x−y\frac{x^3-x^2y+2…