Factor by Grouping

Front

What is 'Factor by Grouping'?

Back

A method used to factor polynomials by grouping terms with common factors.

Front

What is the first step in factoring by grouping?

Back

Group the terms of the polynomial into pairs.

Front

How do you factor the expression x³ - 5x² + 5x - 25?

Back

(x² + 5)(x - 5) is the factored form.

Front

What is the factored form of 8b³ - 4b² + 6b - 3?

Back

(4b² + 3)(2b - 1) is the factored form.

Front

What is the result of factoring x³ + 7x² - 2x - 14?

Back

(x² - 2)(x + 7) is the factored form.

Front

How do you determine if (x + 2) is a factor of 2x³ + 3x² - 8x - 12?

Back

Use synthetic division or the factor theorem; (x + 2) is a factor.

Front

What is the factored form of 9c³ - 12c² + 3c - 4?

Back

(3c² + 1)(3c - 4) is the factored form.

Front

What is a common mistake when factoring by grouping?

Back

Forgetting to factor out the greatest common factor from each group.

Front

What is the role of the greatest common factor in factoring by grouping?

Back

It simplifies the expression before grouping terms.

Front

What does it mean if a polynomial cannot be factored by grouping?

Back

It may be prime or require a different factoring method.