Mixture Factoring Quadratics

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax² + bx + c = 0, 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 is the factored form of x² + 5x - 24?

Back

(x + 8)(x - 3)

Front

How do you factor a quadratic expression of the form x² + bx + c?

Back

To factor, find two numbers that multiply to c and add to b, then rewrite the expression as (x + m)(x + n), where m and n are those numbers.

Front

What is the factored form of x² + 11x + 24?

Back

(x + 8)(x + 3)

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Front

How do you factor the expression 4x² - 81?

Back

Use the difference of squares: (2x - 9)(2x + 9).

Front

What is the factored form of 25x² - 100y²?

Back

(5x - 10y)(5x + 10y) using the difference of squares.

Front

What is the factored form of x² - 25?

Back

(x + 5)(x - 5) using the difference of squares.

Front

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

Back

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