Factoring Quadratics

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

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 is the greatest common factor (GCF)?

Back

The greatest common factor is the largest factor that two or more numbers share.

Front

How do you find the GCF of 42xy² and 28x³y?

Back

The GCF is 14xy.

Front

What is the first step in factoring a quadratic expression?

Back

The first step is to look for the greatest common factor (GCF) of the terms.

Front

Factor the expression: 2c² + 2c - 84.

Back

2(c + 7)(c - 6).

Front

What does it mean to solve by factoring?

Back

To solve by factoring means to rewrite the equation in factored form and then set each factor equal to zero to find the solutions.

Front

Solve the equation by factoring: x² = 7x + 18.

Back

The solutions are x = 9 and x = -2.

Front

Factor the expression: x² + 9x - 36.

Back

(x + 12)(x - 3).