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 are the factors of the expression 5x² + 20x + 20?

Back

5(x+2)(x+2)

Front

How do you factor a difference of squares?

Back

A difference of squares can be factored using the formula a² - b² = (a - b)(a + b).

Front

What are the factors of the expression x² - 81?

Back

(x-9)(x+9)

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What are the roots of the equation 6x² - x - 2 = 0?

Back

x = 2/3, -1/2

Front

What is the process to solve a quadratic equation by factoring?

Back

1. Set the equation to zero. 2. Factor the quadratic expression. 3. Set each factor equal to zero and solve for x.

Front

What are the factors of the expression x² - 8x - 48?

Back

(x-12)(x+4)

Front

What does it mean for a quadratic to be factorable?

Back

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