Factoring Quadratics

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

Front

What is a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does it mean for a quadratic to be factorable?

Back

A quadratic is factorable if it can be expressed as a product of two binomials.

Front

What is the factored form of x² - 9?

Back

(x - 3)(x + 3) - This is an example of a difference of squares.

Front

What is the difference of squares?

Back

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

Front

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

Back

To factor, find two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.

Front

What is the factored form of 5x² + 20x + 20?

Back

5(x + 2)(x + 2) or 5(x + 2)².

Front

What is the factored form of x² - 8x - 48?

Back

(x - 12)(x + 4).

Front

What is the factored form of 25x² - 9?

Back

(5x + 3)(5x - 3) - This is an example of a difference of squares.