Factoring

Front

What is factoring in algebra?

Back

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

Front

What is the factored form of a quadratic expression?

Back

The factored form of a quadratic expression ax² + bx + c is expressed as (px + q)(rx + s), where p, q, r, and s are constants.

Front

Factor the expression: a² - a - 12

Back

(a - 4)(a + 3)

Front

Factor completely: 5x² - 7x + 2

Back

(5x - 2)(x - 1)

Front

Factor the expression: 4x² - 25x + 25

Back

(x - 5)(4x - 5)

Front

Completely factor: 2x² + 18x - 72

Back

2(x + 12)(x - 3)

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a² - b² = (a - b)(a + b).

Front

Factor the expression: 27x³ - 1

Back

(3x - 1)(3x² + 3x + 1)

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

Front

How do you factor by grouping?

Back

To factor by grouping, group terms with common factors, factor out the common factors, and then factor out the common binomial.