Factoring 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, allowing for easier simplification.

Front

What is the first step in factoring by grouping?

Back

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

Front

Factor the expression: 6x² + 9xy + 14x + 21y.

Back

(3x + 7)(2x + 3y)

Front

What is the purpose of factoring polynomials?

Back

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

Front

Factor the expression: 35x² + 5x + 56x + 8.

Back

(5x + 8)(7x + 1)

Front

What does it mean to factor an expression completely?

Back

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

Front

Factor the expression: 70n⁴ + 40n³ + 28n² + 16n.

Back

(10n³ + 4n)(7n + 4)

Front

What is a common factor?

Back

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

Front

Factor the expression: x³ + 7x² + 2x + 14.

Back

(x² + 2)(x + 7)

Front

What is the significance of the distributive property in factoring?

Back

The distributive property allows us to factor out common terms from expressions, making it easier to simplify.