Factor Quadratics

Front

What is the process of factoring quadratics?

Back

Factoring quadratics involves rewriting a quadratic expression in the form ax^2 + bx + c as a product of two binomials (px + q)(rx + s).

Front

Factor the quadratic: x^2 - 9.

Back

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

Front

What is a binomial?

Back

A binomial is a polynomial with two terms, such as (x + 4) or (x - 5).

Front

Factor the quadratic: x^2 + 5x + 6.

Back

(x + 2)(x + 3) - This is found by identifying two numbers that multiply to 6 and add to 5.

Front

What is the zero-product property?

Back

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

Front

Factor the quadratic: x^2 - 4x - 5.

Back

(x - 5)(x + 1) - This is found by identifying two numbers that multiply to -5 and add to -4.

Front

What does it mean to solve a quadratic equation by factoring?

Back

It means to express the quadratic equation in factored form and then use the zero-product property to find the values of x.

Front

Factor the quadratic: x^2 + 7x + 10.

Back

(x + 2)(x + 5) - This is found by identifying two numbers that multiply to 10 and add to 7.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

Factor the quadratic: x^2 - 6x + 8.

Back

(x - 2)(x - 4) - This is found by identifying two numbers that multiply to 8 and add to -6.