Algebra GCF of Polynomials and Prime Factorization

What is the greatest common factor of the terms in the polynomial 12x⁴ + 2x³ –30x²?

• x

• x²

• 2x

• 2x²

Which common factors should be used in the next step of factoring?

• x² and −2x

• 2x² and −2x

• x² and −2

• 2x² and −2

Omar grouped the terms and factored the GCF out of the groups of the polynomial 3x³ – 15x² – 4x + 20. His work is shown.

Step 1: (3x³ – 15x²) + (–4x + 20)

Step 2: 3x²(x – 5) + 4(–x + 5)

Omar noticed that he does not have a common factor. Which accurately describes what Omar should do next?

• Omar should realize that his work shows that the polynomial is prime.

• Omar should go back and regroup the terms in Step 1 as (3x³ – 15x²) – (4x + 20).

• In Step 2, Omar should factor only out of the first expression.

• Omar should factor out a negative from one of the groups so the binomials will be the same.

Factor completely:

3x² + 18x +15

Hint: Factor GCF first.

• 3(x² + 6x + 5)

• (x + 5)(x + 1)

• 3(x + 5)(x + 1)

• Cannot be factored

Factor by GCF:

18a²-15a

• 15a(3a-1)

• 3a(6a-1)

• 3(6a-5)

• 3a(6a-5)

Factor by using GCF:
8n³ + 2n²

• 2n²(4n-1)

• 2n²(4n + 1)

• n²(8n+2)

• 3n(4n+1)

What is the GCF? 5x²+20x

• 5

• x

• 5x

• 20x

Factor by GCF:
4b⁵ + 4b³ + 16b²

• 4b³(b⁴+b²+4b)

• 4b³(b⁴+4b+5)

• 4(b⁵+b³+4b²)

• 4b²(b³+b+4)

Factor by GCF:
6m² + 16m

• 2(3m² + 8m)

• 2m(3m + 8)

• 2m(3m - 8m)

• not factorable

Use a number tree to find the prime factorization of 48

• 4x2x6

• 4x2²x3

• 3x2⁴

• 12x4