Factoring and Quadratic Formula

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

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 ax² + bx + c = 0.

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 express the quadratic as (x + m)(x + n) where m and n are those numbers.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

Factor the expression: r² - 16r + 60

Back

(r - 6)(r - 10)

Front

Factor the expression: 4x² - 25x + 25

Back

(x - 5)(4x - 5)

Front

What does it mean to find the zeros of a quadratic equation?

Back

Finding the zeros means determining the values of x for which the quadratic equation equals zero.

Front

Factor the expression: x² - 4x + 4

Back

(x - 2)(x - 2) or (x - 2)²

Front

Solve for x: 2x² - 8x - 24 = 0

Back

x = 6, -2

Front

Factor completely: 3x² - 8x + 4

Back

(3x - 2)(x - 2)