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.

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

How do you determine if (x - a) is a factor of a polynomial?

Back

To determine if (x - a) is a factor, substitute a into the polynomial. If the result is zero, then (x - a) is a factor.

Tags

CCSS.HSA.APR.B.2

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: x^3 - 5x^2 + 5x - 25

Back

(x^2 + 5)(x - 5)

Front

Factor the expression: x^3 + 7x^2 - 2x - 14

Back

(x^2 - 2)(x + 7)

Front

Factor the expression: 3x^3 - x^2 + 6x - 2

Back

(x^2 + 2)(3x - 1)

Front

Factor the expression: 20x^3 - 25x^2 + 4x - 5

Back

(5x^2 + 1)(4x - 5)

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

Front

What does it mean to factor an expression?

Back

Factoring an expression means to rewrite it as a product of its factors.