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 a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

What does it mean for two expressions to be equivalent?

Back

Two expressions are equivalent if they have the same value for all values of the variable(s) involved.

Front

What is the factored form of a quadratic expression?

Back

The factored form of a quadratic expression is expressed as (px + q)(rx + s), where p, q, r, and s are constants.

Front

How do you factor the expression 3x² + 5x - 12?

Back

The expression factors to (3x - 4)(x + 3).

Front

What is the process to factor x² - 6x + 8?

Back

To factor, find two numbers that multiply to 8 and add to -6. The expression factors to (x - 2)(x - 4).

Front

How do you factor x² - 13x + 40?

Back

Find two numbers that multiply to 40 and add to -13. The expression factors to (x - 5)(x - 8).

Front

What is the factored form of 2x² - 3x - 2?

Back

The expression factors to (2x + 1)(x - 2).

Front

What is the difference of squares?

Back

The difference of squares is a special factoring case where a² - b² = (a - b)(a + b).

Front

How do you factor 25x² - 81?

Back

This expression is a difference of squares and factors to (5x - 9)(5x + 9).