8-5 Factoring Polynomials Using the GCF and Grouping

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest factor that divides two or more numbers or terms without leaving a remainder.

Front

How do you factor a polynomial using the GCF?

Back

To factor a polynomial using the GCF, identify the largest factor common to all terms, then divide each term by the GCF and express the polynomial as the product of the GCF and the resulting polynomial.

Front

Factor the polynomial: 8n³ + 2n²

Back

2n²(4n + 1)

Front

What is the purpose of grouping in polynomial factoring?

Back

Grouping is used to rearrange and group terms in a polynomial to factor by common factors in pairs.

Front

Factor the polynomial: x³ - 4x² - 4x + 16

Back

(x - 4)(x² - 4)

Front

What is the factored form of x³ + 7x² - 2x - 14?

Back

(x² - 2)(x + 7)

Front

Factor the polynomial: 4p³ + 8p² + 3p + 6

Back

(4p² + 3)(p + 2)

Front

What does it mean to factor a polynomial completely?

Back

Factoring a polynomial completely means breaking it down into irreducible factors, where no further factoring is possible.

Front

Factor the expression: 9a²b - 3ab² + 6ab

Back

3ab(3a - b + 2)

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.