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, 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 are the methods for factoring quadratics?

Back

Common methods include factoring by grouping, using the quadratic formula, and recognizing perfect square trinomials.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as (a + b)² = a² + 2ab + b².

Front

How do you factor the expression x² - 10x + 24?

Back

To factor x² - 10x + 24, find two numbers that multiply to 24 and add to -10. The factors are (x - 4)(x - 6).

Front

What is the factored form of x² + 16x + 15?

Back

The factored form is (x + 1)(x + 15).

Front

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

Back

To factor, look for two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the middle term and factor by grouping.

Front

What is the significance of the leading coefficient in a quadratic expression?

Back

The leading coefficient (a) affects the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What is the difference between factoring and expanding?

Back

Factoring is breaking down an expression into products, while expanding is multiplying out the factors to get back to the original expression.