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 used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

Factor the expression: r² - 16r + 60

Back

(r - 6)(r - 10)

Front

Factor completely: 3x² - 8x + 4

Back

(3x - 2)(x - 2)

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down an expression into its simplest factors, where no further factoring is possible.

Front

Factor the expression: 3x² - 36x + 96

Back

3(x - 4)(x - 8)

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.

Front

Factor the expression: 4x² - 25x + 25

Back

(x - 5)(4x - 5)

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, which determines the nature of the roots.

Front

How do you determine if a quadratic can be factored?

Back

A quadratic can be factored if its discriminant (b² - 4ac) is a perfect square.