Factoring Polynomials (Grouping and Sum/Difference of Cubes)

Front

What is the formula for factoring the sum of cubes, a³ + b³?

Back

(a + b)(a² - ab + b²)

Front

What is the formula for factoring the difference of cubes, a³ - b³?

Back

(a - b)(a² + ab + b²)

Front

What is the first step in factoring by grouping?

Back

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

Front

What is a perfect square?

Back

A number that can be expressed as the square of an integer.

Front

What is a perfect cube?

Back

A number that can be expressed as the cube of an integer.

Front

Factor the polynomial: 216x³ + 125

Back

(6x + 5)(36x² - 30x + 25)

Front

Factor the polynomial: 125x³ - 64

Back

(5x - 4)(25x² + 20x + 16)

Front

What is the result of factoring 20x³ - 25x² + 4x - 5 by grouping?

Back

(5x² + 1)(4x - 5)

Front

Identify a number that is both a perfect square and a perfect cube.

Back

64

Front

What is the significance of the coefficients in a polynomial when factoring?

Back

They can indicate common factors and help simplify the expression.