Section 4.1 - Solve Quadratic Equations by Factoring

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 does it mean to solve a quadratic equation by factoring?

Back

Solving a quadratic equation by factoring involves expressing the equation in the form (px + q)(rx + s) = 0 and finding the values of x that make each factor equal to zero.

Front

What are the roots of the equation x² + 4x - 32 = 0?

Back

The roots are -8 and 4.

Front

How do you factor the quadratic x² + 3x - 18?

Back

To factor, find two numbers that multiply to -18 and add to 3. The factors are (x - 6)(x + 3).

Front

What are the roots of the equation x² + 3x - 18 = 0?

Back

The roots are -6 and 3.

Front

What is the factored form of the quadratic equation x² - 14x - 51?

Back

The factored form is (x - 17)(x + 3).

Front

What are the roots of the equation x² - 14x - 51 = 0?

Back

The roots are -3 and 17.

Front

How do you factor the quadratic 5x² + 13x + 6?

Back

To factor, find two numbers that multiply to 30 (5*6) and add to 13. The factors are (5x + 3)(x + 2).

Front

What are the roots of the equation 5x² + 13x + 6 = 0?

Back

The roots are -2 and -3/5.

Front

How do you factor the quadratic 6x² - x - 2?

Back

To factor, find two numbers that multiply to -12 (6*-2) and add to -1. The factors are (3x + 2)(2x - 1).