Factoring Quadratics

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of two binomials.

Front

What are the steps to factor a quadratic expression of the form x² + bx + c?

Back

1. Identify two numbers that multiply to c and add to b. 2. Rewrite the expression as (x + m)(x + n), where m and n are the identified numbers.

Front

How do you factor the quadratic expression x² + 11x + 24?

Back

To factor x² + 11x + 24, find two numbers that multiply to 24 and add to 11, which are 8 and 3. Thus, it factors to (x + 8)(x + 3).

Front

What is the factored form of x² + 3x - 4?

Back

The factored form of x² + 3x - 4 is (x + 4)(x - 1).

Front

What is the difference between factoring and expanding a quadratic expression?

Back

Factoring is rewriting the expression as a product of factors, while expanding is multiplying the factors to return to the original expression.

Front

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

Back

The leading coefficient (a) determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

How can you check if your factored form of a quadratic expression is correct?

Back

You can check by expanding the factored form to see if it matches the original quadratic expression.

Front

What is the role of the discriminant in factoring quadratics?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What are the common methods for factoring quadratics?

Back

Common methods include factoring by grouping, using the quadratic formula, and completing the square.