Factoring Quadratics

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, 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 are the steps to factor a quadratic expression?

Back

1. Identify a, b, and c from the expression ax² + bx + c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the expression using these numbers. 4. Factor by grouping.

Front

Factor the expression: x² + 11x + 24

Back

(x + 8)(x + 3)

Front

Factor the expression: x² + 5x - 24

Back

(x + 8)(x - 3)

Front

Factor the expression: x² + 9x - 36

Back

(x + 12)(x - 3)

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 check if your factors are correct?

Back

You can check by multiplying the factors back together to see if you obtain the original quadratic expression.

Front

What is the significance of the coefficients in a quadratic expression?

Back

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic expression.

Front

What does it mean for a quadratic to be factorable?

Back

A quadratic is factorable if it can be expressed as the product of two binomials with real coefficients.