Factor by Grouping

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials with four or more terms by grouping terms in pairs and factoring out the common factors.

Front

How do you identify common factors in a polynomial?

Back

To identify common factors, look for terms that share a common variable or numerical coefficient. Factor out the greatest common factor (GCF) from the grouped terms.

Front

What is the first step in factoring by grouping?

Back

The first step is to group the terms of the polynomial into pairs.

Front

Factor by grouping: x³ + 7x² - 2x - 14

Back

(x² - 2)(x + 7)

Front

Factor by grouping: x³ - 4x² - 4x + 16

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(x - 4)(x² - 4)

Front

How many terms are in the polynomial 2x³ - 8x² + 3x - 7?

Back

4

Front

Factor by grouping: 4p³ + 8p² + 3p + 6

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(4p² + 3)(p + 2)

Front

Factor by grouping: 5n³ - 10n² + 3n - 6

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(5n² + 3)(n - 2)

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which can be simpler polynomials or numbers.