Factoring and Solving Quadratics

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 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 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: 49x² - 100

Back

(7x - 10)(7x + 10)

Front

What are the factors of x² + 3x - 40?

Back

(x + 8)(x - 5)

Front

Solve for z: z² - 14z + 45 = 0

Back

z = 5, 9

Front

Solve using the Zero-Product Property: 7x(x - 6) = 0

Back

x = 0 and x = 6

Front

Solve the equation: m² - 100 = 0

Back

m = 10, -10

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac, which determines the nature of the roots.