Factoring Quadratics

Front

What is factoring in algebra?

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.

Front

What are the common methods for factoring quadratics?

Back

Common methods include factoring by grouping, using the quadratic formula, and recognizing special products.

Front

What is the factored form of a quadratic expression?

Back

The factored form of a quadratic expression is expressed as (px + q)(rx + s), where p, q, r, and s are constants.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you factor a quadratic expression of the form x² + bx + c?

Back

To factor, find two numbers that multiply to c and add to b, then express as (x + m)(x + n).

Front

What are the factors of x² - 8x - 48?

Back

(x - 12)(x + 4) are the factors.

Front

What are the factors of 3x² - 17x + 10?

Back

(x - 5)(3x - 2) are the factors.

Front

What is the factored form of 25x² - 9?

Back

(5x + 3)(5x - 3) is the factored form.

Front

What are the factors of x² + 3x - 40?

Back

(x + 8)(x - 5) are the factors.