8-5: Factoring

Front

What is factoring in algebra?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

What are the factors of x² - 16?

Back

(x - 4)(x + 4) - This is a difference of squares.

Front

How do you factor x² + 8x - 20?

Back

(x + 10)(x - 2) - Find two numbers that multiply to -20 and add to 8.

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / 2a - Used to find the roots of a quadratic equation.

Front

What does it mean for an expression to be prime?

Back

An expression is prime if it cannot be factored into simpler expressions with integer coefficients.

Front

How do you factor x² + 2x - 3?

Back

(x - 1)(x + 3) - Find two numbers that multiply to -3 and add to 2.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic in the form (x - p)² = q to make it easier to solve.

Front

What are the steps to factor a quadratic expression?

Back

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

Front

What is the factored form of x² - 6x + 10?

Back

This expression cannot be factored over the integers; it is prime.