Math II 4.2.1 Warm UP

Front

What is the process of factoring a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it as a product of two binomials. This is done by finding two numbers that multiply to the constant term and add to the coefficient of the linear term.

Front

What is the factored form of the expression x² + 9x - 36?

Back

(x + 12)(x - 3)

Front

How do you factor the expression 3x² - 75?

Back

First, factor out the greatest common factor (GCF), which is 3, resulting in 3(x² - 25). Then, recognize that x² - 25 is a difference of squares, which factors to (x + 5)(x - 5). Thus, the complete factorization is 3(x + 5)(x - 5).

Front

What is the factored form of a² - a - 12?

Back

(a - 4)(a + 3)

Front

How do you factor the expression x² + 4xy + 4y²?

Back

This expression is a perfect square trinomial, which factors to (x + 2y)(x + 2y) or (x + 2y)².

Front

What is the difference of squares, and how is it factored?

Back

The difference of squares is a special case of factoring that applies to expressions of the form a² - b². It can be factored as (a + b)(a - b).

Front

What is the factored form of 25x² - 81?

Back

(5x + 9)(5x - 9), which is a difference of squares.

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as x + 2 or 3a - 5.

Front

What is a trinomial?

Back

A trinomial is a polynomial that contains exactly three terms, such as x² + 5x + 6.

Front

What is the greatest common factor (GCF) and how is it used in factoring?

Back

The GCF is the largest factor that divides all terms in a polynomial. It is used in factoring by first factoring out the GCF from the polynomial before further factoring the remaining expression.