Factoring Polynomials Review

Factoring Polynomials

What should I check for first?

1. Difference of Squares
2. Greatest Common Factor (GCF)
3. Basic Trinomial (x² + bx + c)
4. Grouping Method / AC Method (ax² + bx + c)

Difference of Squares

Multiple Choice

Factor: $$9x^2-25$$

• $$\left(3x+5\right)\left(3x-5\right)$$

• $$\left(3x+5\right)^2$$

• $$\left(3x-5\right)^2$$

Multiple Select

Which of the following are examples of difference of squares?

• $$16x^2+24x+9$$

• $$36x^2-100$$

• $$16x^2+49$$

• $$25x^2-81$$

• $$x^2+6x+9$$

Greatest Common Factor (GCF)

Math Response

Factor the polynomial completely.

$$5x^2+30x$$

Type answer here

Correct Answer: 5x\left(x+6\right)

Deg^°

Rad

Multiple Choice

Katherine was factoring the polynomial $$42c^2-15c$$ but one of the terms got erased. Which of the following could be the missing factor?

___ $$\left(14c-5\right)$$

• 3c

• 3

• -3c

• c-3

Basic Trinomial
(x² + bx + c)

Multiple Choice

Which expression is a factor of the following trinomial?

$$x^2-7x-8$$

• $$\left(x+1\right)$$

• $$\left(x+8\right)$$

• $$\left(x+2\right)$$

• $$\left(x-4\right)$$

Multiple Choice

Which function is equivalent to $$k\left(x\right)=x^2+2x-15$$ ?

• $$k\left(x\right)=\left(x+15\right)\left(x-1\right)$$

• $$k\left(x\right)=\left(x+1\right)\left(x-15\right)$$

• $$k\left(x\right)=\left(x+5\right)\left(x-3\right)$$

• $$k\left(x\right)=\left(x+3\right)\left(x-5\right)$$

Multiple Choice

Factor the following trinomial.

$$x^2+20x+100$$

• $$\left(x+10\right)^2$$

• $$\left(x-10\right)^2$$

• $$\left(x+10\right)\left(x-10\right)$$

• $$\left(x+50\right)^2$$

Grouping Method / AC Method (ax² + bx + c)

Math Response

Factor the trinomial completely.

$$10x^2-17x+6$$

Type answer here

Correct Answer: \left(2x-1\right)\left(5x-6\right)

Deg^°

Rad

Multiple Choice

Which function is equivalent to $$r\left(x\right)=3x^2-13x+12$$

• $$r\left(x\right)=\left(x-3\right)\left(3x-4\right)$$

• $$r\left(x\right)=\left(x-3\right)\left(3x+4\right)$$

• $$r\left(x\right)=\left(3x+1\right)\left(x+12\right)$$

• $$\left(3x-1\right)\left(x-12\right)$$