Factoring Polynomials Using GCF

GCF, Factoring Polynomials, & Grouping

By Ms. Costa

We multiplied polynomials using distributive property.

Now we can work backward and pull a monomial factor out of a polynomial​

​

Use the distributive property​

​1.6w² + 6w

Factor 4y²-24y

• All terms can be divided by 4, and all terms contain at least 1 y.

• We factor OUT a 4y and the leftovers stay in the parentheses.

• 4y(y-6)

Multiple Choice

What is the Greatest Common Factor of 18 and 54?

• 9

• 6

• 54

• 18

• 3

Fill in the Blank

The greatest common factor (GCF) of 48 and 36 is

Fill in the Blank

What is the greatest common factor of 12x and 18x?

Multiple Choice

15w - 3v

• 5(3w - 3v)

• 3w(5 - 3v)

• 3(5w - v)

• 3v(5w)

Multiple Choice

Factor by GCF:

6m² + 16m

• 2(3m² + 8m)

• 2m(3m + 8)

• 2m(3m - 8m)

• Prime

Multiple Choice

Factor
4b⁵+4b³+16b²

• 4b³(b⁴+b²+4b)
• 4b³(b⁴+4b+5)
• 4(b⁵+b³+4b²)
• 4b²(b³+b+4)

Multiple Choice

Factor:
 2n²-8n³

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

Multiple Choice

7u²t² + 21ut² - ut

• 7(u²t² + 3ut² - ut)

• ut(7ut + 21t - 1)

• u(7ut² + 21t² - t)

• t(7u²t + 21ut - u)

Multiple Choice

Factor: 3x² + 4x

• x(3x + 4)

• 3x(x + 4x)

• 3(x² +4x)

• x²(3+4)

Multiple Choice

Factor 2x² + 4x – 3x – 6 by grouping. Remember to look for common factors first.

• (2x – 3)(x + 2)

• 2x² + x - 6

• (2x + 3)(x - 2)

Multiple Choice

Factor by grouping:

5n³-10n²+3n-6

• (5n²+3)(n-2)

• (5n³+3)(n-2)

• (5n²-3)(n-2)

• 10n(n²-6)

Multiple Choice

Factor 28x² + 63x + 12x + 27 by grouping. Remember to look for common factors first.

• (4x + 3)(7x + 9)

• (7x + 3)(4x + 9)

• (3x + 7)(4x + 9)

• (9x + 4)(3x + 7)