Factor by Grouping

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms with common factors together.

Front

What is the first step in factoring by grouping?

Back

The first step is to group the terms of the polynomial into pairs or sets that have common factors.

Front

Factor the expression: 20x³ - 25x² + 4x - 5

Back

(5x² + 1)(4x - 5)

Front

Factor the expression: 5n³ - 10n² + 3n - 6

Back

(5n² + 3)(n - 2)

Front

What is a common factor?

Back

A common factor is a number or variable that divides two or more terms evenly.

Front

How do you check if your factoring is correct?

Back

You can check by multiplying the factors back together to see if you get the original expression.

Front

Factor the expression: 2x³ - 8x² - x + 4

Back

(2x² - 1)(x - 4)

Front

What is the purpose of factoring polynomials?

Back

The purpose is to simplify expressions, solve equations, and find roots.

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down a polynomial into its simplest factors that cannot be factored further.

Front

What is the relationship between factoring and solving equations?

Back

Factoring can help solve equations by setting each factor equal to zero to find the roots.