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, or factors, that when multiplied together give the original expression.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

Factor the expression: 4x² - 25x + 25

Back

(x - 5)(4x - 5)

Front

Factor completely: 3x² - 36x + 96

Back

3(x - 4)(x - 8)

Front

Solve for x: 2x² - 8x - 24 = 0

Back

x = 6, -2

Front

Factor the expression: r² - 16r + 60

Back

(r - 6)(r - 10)

Front

Solve the equation: x² + 4x - 40 = -8

Back

x = -8 & x = 4

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants.

Front

What does it mean to factor completely?

Back

To factor completely means to break down an expression into its simplest factors, such that no further factoring is possible.

Front

What is the discriminant in the quadratic formula?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots of the quadratic equation.