Square Box Problems and 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 GCF (Greatest Common Factor)?

Back

The GCF is the largest factor that two or more numbers have in common.

Front

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

Back

To factor a quadratic expression, find two numbers that multiply to c and add to b, then express the quadratic as (x + m)(x + n) where m and n are the two numbers.

Front

Factor the expression: x² - 10x - 24

Back

(x - 12)(x + 2)

Front

What is the negative GCF?

Back

The negative GCF is the largest common factor of a set of terms, taken as a negative value, used to factor out the expression.

Front

Factor completely using the negative GCF: -6x + 36xy - 12

Back

-6(x - 6xy + 2)

Front

What does it mean to factor by GCF?

Back

Factoring by GCF involves identifying the greatest common factor of all terms in an expression and factoring it out.

Front

Factor by GCF: 10a⁴ + 16a + 10a²

Back

2a(5a³ + 8 + 5a)

Front

How do you factor the expression -2x - 2y?

Back

-2(x + y)

Front

What is the diamond (or X) method in factoring?

Back

The diamond method is a visual technique used to find two numbers that multiply to the product of the leading coefficient and the constant term, and add to the middle coefficient.