Factor by Grouping Practice

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms with common factors together.

Front

How do you identify common factors in a polynomial?

Back

Look for terms that share a common variable or numerical coefficient, and group them accordingly.

Front

Factor the expression: 5n³ - 10n² + 3n - 6

Back

(5n² + 3)(n - 2)

Front

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

Back

(5x² + 1)(4x - 5)

Front

What is the first step in factoring by grouping?

Back

The first step is to group the polynomial into two parts that can be factored separately.

Front

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

Back

(2x² - 1)(x - 4)

Front

What does it mean for a binomial to be a factor of a polynomial?

Back

A binomial is a factor of a polynomial if the polynomial can be divided by the binomial without leaving a remainder.

Front

Determine if (3v - 7) is a factor of 3v² + 3v - 7v - 7.

Back

Yes, it is a factor.

Front

Factor the expression: 4p³ + 8p² + 3p + 6

Back

(4p² + 3)(p + 2)

Front

What is the significance of the greatest common factor (GCF) in factoring?

Back

The GCF is the largest factor that can be factored out from all terms in a polynomial, simplifying the expression.