Factoring GCF and Quadratics

GCF Factoring

What is the GCF?

GCF stands for Greatest Common Factor. It is the largest number that goes into the numbers in question.

For example: The GCF of 24 and 36 is 12. That's because 12 is the largest number that goes into 24 and 36 evenly.

Multiple Choice

What is the GCF of 16 and 20?

• 2

• 4

• 5

• 16

Multiple Choice

What is the GCF of 18, 27, and 36?

• 2

• 3

• 9

• 18

What is factoring?

Factoring is rewriting a polynomial as a product of it's factors.

Multiple Select

Which expression represents a FACTORED form? Pick ALL that applies

• $$x^2-3x+4$$

• $$x^2\left(x-3\right)$$

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

• $$3x^4-5y$$

Factoring out the GCF of a polynomial.

To factor out a GCF from a polynomial we do the following:

1. Find the GCF.

2. Divide the polynomial by the GCF.

3. Rewrite the polynomial as the product of the GCF and the quotient we got when we divided the polynomial by the GCF.

4. Check your work by multiplying.

Multiple Choice

What is the GCF of 18x and 15x³

• 3x²

• 3x³

• 3x

• 5x

Multiple Choice

Let's try to factor out GCF $$4x^3-x$$

Step 1. Find the GCF.

• 4

• x

• 3

• -1

Multiple Choice

$$\frac{4x^3}{x}-\frac{x}{x}$$

Step 2. Divide the polynomial by the GCF. What is left?

• $$\left(4x^2-1\right)$$

• $$4x^2$$

• 4

• x

Multiple Choice

$$4x^3-x$$

Step 3. Rewrite the polynomial as the product of the GCF and the quotient

• $$x\left(4x^2-1\right)$$

• $$4\left(x^3-1\right)$$

• $$x+4x^2-1$$

• $$4\left(x^3-1\right)$$

Multiple Choice

Let's try another one

$$Factor\ GCF\ out\ \ \ of\ \ \ 3x^2+6x$$

Step 1. Find the GCF first

• 3

• 6

• 3x

• 6x

Multiple Choice

$$3x^2+6x$$

Step 2. Divide each term by GCF

$$\frac{3x^2}{3x}+\frac{6x}{3x}$$

• (3x+6)

• (x+2)

• (x+2x)

• $$\left(x^2+2\right)$$

Multiple Choice

$$3x^2+6x$$

Step 3: Rewrite the polynomial as the product of the GCF and the quotient

• 3x(x+6)

• $$3\left(x^2+6\right)$$

• $$x\left(3+6x\right)$$

• $$3x\left(x+2\right)$$

Multiple Choice

Factor:
p² - 14p

• p(1 - 14)
• 2p(p - 7)
• p²(1-14)
• p(p - 14)

Multiple Choice

Factor:
 2n²-8n³

• 2n²(n-4n²)
• 2n²(1-4n)
• 2n³(10-8n²)
• 3n(1-4n)

Multiple Choice

Factor 4x - 20

• 4(x -5)
• 4(x + 5)
• 4x(1 - 5)
• 4x(1 + 5)