Mixed Factoring

Front

What is mixed factoring?

Back

Mixed factoring is the process of factoring expressions that may involve both numerical coefficients and variables, often requiring the use of different factoring techniques such as grouping, common factors, and special products.

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to look for the greatest common factor (GCF) of all the terms in the polynomial and factor it out.

Front

Factor the expression: 56a³ - 8a.

Back

8a(7a² - 1)

Front

How do you factor a quadratic expression in the form ax² + bx + c?

Back

To factor a quadratic expression in the form ax² + bx + c, look for two numbers that multiply to ac and add to b, then rewrite the expression using these numbers.

Front

Factor completely: 2k² - 14k - 60.

Back

2(k - 10)(k + 3)

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a² - b² = (a - b)(a + b).

Front

Factor the expression: 7r³ - 8r² + 42r - 48.

Back

(r² + 6)(7r - 8)

Front

What is the purpose of factoring in algebra?

Back

Factoring is used to simplify expressions, solve equations, and find roots of polynomials.

Front

Factor the expression: 2m² + 3m - 9.

Back

(m + 3)(2m - 3)

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables raised to non-negative integer powers and coefficients.