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

Why is factoring important in algebra?

Back

Factoring is important because it simplifies expressions and helps solve equations more easily.

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: 2x^2 + 4x + 3x + 6

Back

(2x^2 + 4x) + (3x + 6) = 2x(x + 2) + 3(x + 2) = (2x + 3)(x + 2)

Front

What does it mean to factor out a common factor?

Back

Factoring out a common factor means to divide each term in a polynomial by the greatest common factor (GCF) and express the polynomial as a product.

Front

Factor the expression: 6x^3 + 9x^2

Back

3x^2(2x + 3)

Front

What is a polynomial?

Back

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

Front

Factor the expression: x^2 - 9

Back

(x - 3)(x + 3)

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern where a^2 - b^2 = (a - b)(a + b).

Front

Factor the expression: x^3 - 3x^2 + 3x - 9

Back

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