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 does it mean to factor a quadratic expression?

Back

To factor a quadratic expression means to express it as a product of two binomials.

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 is the quadratic formula?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots of the quadratic equation: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

How do you factor a quadratic expression when a = 1?

Back

When a = 1, factor the expression x² + bx + c by finding two numbers that multiply to c and add to b.

Front

How do you factor a quadratic expression when a ≠ 1?

Back

When a ≠ 1, use the method of grouping or the ac method: multiply a and c, find two numbers that multiply to ac and add to b, then rewrite and factor by grouping.

Front

What is the factored form of 3v² - 4v - 7?

Back

(3v - 7)(v + 1)

Front

What is the factored form of 5x² - 28x + 32?

Back

(5x - 8)(x - 4)