Factoring Polynomials

Which expression(s) have a greatest common factor (GCF) of 3xy² with 42xy⁴? Select all that apply.

• 6x²y²

• 15xy²z

• 27x³y²

• 9xy³

Factor out the GCF from the terms of the polynomial −2x⁵ − 6x³ − 16x².

• −2x(x⁴ + 3x² + 8x)

• −2x²(x³ + 3x + 8)

• −2x²(−x³ − 3x − 8)

• The polynomial is already fully factored.

Factor out the GCF from the terms of the polynomial 2x³ − 5x² + 25.

• x²(2x − 5) + 25

• The polynomial is already fully factored.

• 2x³ − 5(x² − 5)

• .2(x³ − 2.5x² + 12.5)

Identify a pair of factors of −35 that has a sum of −2.

• 5 and -7

• -5 and 7

• -5 and -7

• 5 and 7

Enter a number in each box to write the factored form of y² + 11y + 28.

• (y+4)(y-7)

• (y+3)(y+7)

• (y-2)(y+14)

• (y+4)(y+7)

What is the factored form of x² − 9x + 20?

• x(x − 9) + 20

• (x − 4)(x + 5)

• (x − 4)(x − 5)

• (x² − 4)(x² − 5)

What is the factored form of x² + 4xy − 21y²?

• xy(x + 4 − 21y)

• (x − 3y)(x + 7y)

• x(x + 4y) + y(4x − 21y)

• (x + 3y)(x − 7y)

What is the factored form of 2x³ + 4x² − 30x?

• 2x(x − 5)(x + 3)

• (x² + 5)(2x − 6)

• x(2x + 10)(2x − 6)

• 2x(x + 5)(x − 3)

Which trinomial below has a factor of (x + 2) and (3x – 3)?

• 3x² – 6

• 3x² + 3x – 6

• 3x² + 6x – 6

• 3x2²+ 9x – 6

When factored completely, the expression 2x² + 10x - 12 is equivalent to which of the expressions below?

• 2(x-6)(x+1)

• 2(x+6)(x-1)

• 2(x+2)(x+3)

• 2(x-2)(x-3)