Factoring Polynomials

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

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)