4.4 Factoring Quadratic Expressions

Front

What is the general form of a quadratic expression?

Back

The general form of a quadratic expression is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of two binomials.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Tags

CCSS.HSA.APR.C.4

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, find two numbers that multiply to ac and add to b, then rewrite the expression using these numbers.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial, such as (a + b)² = a² + 2ab + b².

Tags

CCSS.HSA.APR.C.4

Front

How do you determine if a quadratic expression is factorable?

Back

A quadratic expression is factorable if its discriminant (b² - 4ac) is a perfect square.

Tags

CCSS.HSA-REI.B.4B

Front

What is the factored form of the expression 4x² - 9y²?

Back

The factored form of 4x² - 9y² is (2x - 3y)(2x + 3y), using the difference of squares.

Tags

CCSS.HSA.APR.C.4

Front

What are the steps to factor the expression x² + 13x + 30?

Back

To factor x² + 13x + 30, find two numbers that multiply to 30 and add to 13, which are 3 and 10. Thus, it factors to (x + 3)(x + 10).

Front

What is the value of c that makes x² + 2x + c a perfect square trinomial?

Back

The value of c that makes x² + 2x + c a perfect square trinomial is 1, since (x + 1)² = x² + 2x + 1.

Tags

CCSS.HSA.APR.C.4

Front

How do you factor the expression 4x² - 16x - 9?

Back

To factor 4x² - 16x - 9, find two numbers that multiply to (4)(-9) = -36 and add to -16. The factors are (2x - 9)(2x + 1).