AB-Solving Quadratics by Factoring

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation means expressing it as a product of two binomials, such as (x - p)(x - q) = 0, where p and q are the roots of the equation.

Tags

CCSS.HSA-REI.B.4B

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

How do you find the roots of a quadratic equation by factoring?

Back

To find the roots, factor the quadratic into the form (x - p)(x - q) = 0, then set each factor equal to zero: x - p = 0 and x - q = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What is the relationship between the coefficients and the roots of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots (p + q) is -b/a and the product of the roots (pq) is c/a.

Tags

CCSS.HSA-REI.B.4B

Front

Solve by factoring: x² + 9x + 20 = 0

Back

x = -4, x = -5

Tags

CCSS.HSA-REI.B.4B

Front

Solve by factoring: x² + 12 = -7x

Back

x = -3, x = -4

Tags

CCSS.HSA-REI.B.4B

Front

Solve by factoring completely: 3x² + 9x - 54 = 0

Back

x = 3, x = -6

Tags

CCSS.HSA-REI.B.4B

Front

Solve by factoring completely: 2x² - 18x + 40 = 0

Back

x = 4, x = 5

Tags

CCSS.HSA-REI.B.4B

Front

Solve: 16a² - 9 = 0

Back

a = -3/4, a = 3/4

Tags

CCSS.HSA-REI.B.4B