Factoring by grouping

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms in pairs and factoring out the common factors from each pair.

Front

How do you factor the expression x^3 + 7x^2 - 2x - 14 by grouping?

Back

Group the terms: (x^3 + 7x^2) + (-2x - 14). Factor out common factors: x^2(x + 7) - 2(x + 7). The factored form is (x^2 - 2)(x + 7).

Front

What is the first step in factoring by grouping?

Back

The first step is to rearrange the polynomial into groups that can be factored easily.

Front

When factoring the polynomial 6n^3 + 3n^2 + 8n + 4, what common factor can be factored out from the first two terms?

Back

The common factor from the first two terms (6n^3 + 3n^2) is 3n^2.

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What is the result of factoring the polynomial 3x^3 - 4x^2 + 9x - 12?

Back

The result is (x^2 + 3)(3x - 4).

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How can you verify if (5x - 4) is a factor of the polynomial 5x^3 - 4x^2 - 25x + 20?

Back

You can use polynomial long division or synthetic division to divide the polynomial by (5x - 4). If the remainder is 0, then it is a factor.

Tags

CCSS.HSA.APR.B.2

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms.

Front

What is the significance of finding common factors in factoring by grouping?

Back

Finding common factors allows you to simplify the polynomial and make it easier to factor completely.

Front

What is the factored form of the polynomial 12x^3 + 2x^2 - 30x - 5?

Back

The factored form is (2x^2 - 5)(6x + 1).

Front

What does it mean if a polynomial is factorable?

Back

A polynomial is factorable if it can be expressed as a product of two or more polynomials of lower degree.