Solving Quadratic Equations by Factoring General Trinomial

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic trinomial?

Back

Factoring a quadratic trinomial involves rewriting it as a product of two binomials, such as (x + p)(x + q), where p and q are numbers that satisfy the equation.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + 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 - r1)(x - r2) = 0, then set each factor equal to zero and solve for x.

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 ax^2 + bx + c = 0, the sum of the roots (r1 + r2) is -b/a and the product of the roots (r1 * r2) is c/a.

Tags

CCSS.HSA-REI.B.4B

Front

Solve the quadratic equation by factoring: x^2 + 8x + 15 = 0

Back

x = -3, -5

Tags

CCSS.HSA-REI.B.4B

Front

Factor the quadratic trinomial: x^2 + 5x + 6

Back

(x + 2)(x + 3)

Front

Factor the quadratic trinomial: 4x^2 - 12x + 9

Back

(2x - 3)(2x - 3)

Front

Solve the quadratic equation by factoring: x^2 - 4x - 5 = 0

Back

x = 5, -1

Tags

CCSS.HSA-REI.B.4B

Front

Solve the quadratic equation by factoring: 3x^2 - 10x - 8 = 0

Back

x = -2/3, 4

Tags

CCSS.HSA-REI.B.4B