Solving by Factoring (a>1)

Front

What is the Zero-Product Property?

Back

If the product of two factors is zero, then at least one of the factors must be zero.

Front

Solve using the Zero-Product Property: (x − 11)(5x + 1) = 0

Back

x = 11 or x = -\frac{1}{5}

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components (factors) that, when multiplied together, give the original expression.

Front

Solve by factoring: 2x^2 - 5x - 12 = 0

Back

x = 4 and x = -\frac{3}{2}

Front

What is a quadratic equation?

Back

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

Front

Factor and Solve: m^2 − 100 = 0

Back

m = 10, m = -10

Front

What are the steps to factor a quadratic equation?

Back

1. Write the equation in standard form. 2. Identify a, b, and c. 3. Find two numbers that multiply to ac and add to b. 4. Rewrite the equation and factor.

Front

Find the factors of 4x^2 - 16x - 9

Back

(2x - 9)(2x + 1)

Front

Solve by factoring: 6x^2 - x - 2 = 0

Back

x = \frac{2}{3}, x = -\frac{1}{2}

Front

What is the relationship between the roots and the factors of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero, and they correspond to the factors of the polynomial.