Factor by Grouping and GCF

Front

What is the definition of GCF (Greatest Common Factor)?

Back

The GCF of two or more numbers is the largest number that divides all of them without leaving a remainder.

Front

How do you find the GCF of 18k and 15k³?

Back

The GCF is 3k, as 3 is the largest common factor of 18 and 15, and k is the lowest power of k present in both terms.

Front

What is the first step in factoring by grouping?

Back

Group the terms in pairs and factor out the common factor from each pair.

Front

Factor the expression: 2x³ - 8x² - x + 4

Back

(2x² - 1)(x - 4)

Front

What does it mean to factor by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors.

Front

Factor the expression using GCF: 17xy - x

Back

x(17y - 1)

Front

What is the GCF of 20 and 25?

Back

The GCF is 5.

Front

Factor the expression: x³ + 7x² - 2x - 14

Back

(x² - 2)(x + 7)

Front

What is the GCF of the coefficients in the expression 20x³ - 25x² + 4x - 5?

Back

The GCF of the coefficients 20, -25, 4, and -5 is 1.

Front

Factor the expression: 20x³ - 25x² + 4x - 5

Back

(5x² + 1)(4x - 5)