Factoring by Grouping and Perfect Cubes

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms with common factors and then factoring out the common binomial.

Front

What is a perfect cube?

Back

A perfect cube is a number that can be expressed as the cube of an integer. For example, 1, 8, 27, and 64 are perfect cubes (1³, 2³, 3³, 4³ respectively).

Front

What is the factored form of 5n³-10n²+3n-6?

Back

(5n²+3)(n-2)

Front

How do you factor a sum of cubes?

Back

To factor a sum of cubes, use the formula a³ + b³ = (a + b)(a² - ab + b²).

Front

What is the factored form of x³ + 1?

Back

(x + 1)(x² - x + 1)

Front

What is the factored form of x³ + 7x² - 2x - 14?

Back

(x² - 2)(x + 7)

Front

What is the formula for factoring a difference of cubes?

Back

The formula for factoring a difference of cubes is a³ - b³ = (a - b)(a² + ab + b²).

Front

What is the factored form of 27x³ - 64?

Back

(3x - 4)(9x² + 12x + 16)

Front

What is the factored form of 4p³ + 8p² + 3p + 6?

Back

(4p² + 3)(p + 2)

Front

What is the first step in factoring by grouping?

Back

The first step is to group the terms in pairs and factor out the common factor from each pair.