Factoring Polynomials by Groups

• Combine like terms.

• Group the terms into two pairs.

• Factor out the greatest common factor of all terms.

• Expand the polynomial.

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

• x² and −2x

• 2x² and −2x

• x² and −2

• 2x² and −2

The polynomial 24x³ − 54x² + 44x − 99 is factored by grouping.

• 6x + 11

• 6x − 11

• 6x² + 11

• 6x² − 11

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.

Mathematical Equivalence

ON

Mathematical Equivalence

ON

Mathematical Equivalence

ON

What is the factorization of 81a⁶ - 100?

• (9a² − 10)(9a³ + 10)

• (9a² − 10)(9a³ − 10)

• (9a³ − 10)(9a³ + 10)

• (9a³ − 10)(9a³ − 10)

Which product of prime polynomials is equivalent to 4x⁵ – 6x⁴ + 4x³ – 6x²?

• 2x²(x² + 1)(2x – 3)

• 2x²(x² – 1)(2x + 3)

• x²(x² + 1)(2x – 3)

• 2(x² – 1)(2x + 3)