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 is typically written as (ax + b)(cx + d), where a, b, c, and d are constants.

Front

Factor completely: 3x² + 18x + 15

Back

3(x + 5)(x + 1)

Front

Factor completely: 2x² + 22x + 60

Back

2(x + 5)(x + 6)

Front

Factor: x² + 7x + 12

Back

(x + 3)(x + 4)

Front

Factor: x² + 9x - 36

Back

(x + 12)(x - 3)

Front

Factor: d² - 10d + 25

Back

(d - 5)(d - 5)

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

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that two or more numbers or expressions share.

Front

How do you factor a trinomial of the form x² + bx + c?

Back

To factor a trinomial of the form x² + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n), where m and n are those two numbers.