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 Factor by Grouping?

Back

Identify and group terms that have common factors.

Front

How do you factor the expression 7r³ - 8r² + 42r - 48?

Back

(r² + 6)(7r - 8) is the factored form.

Front

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

Back

(4p² + 3)(p + 2) is the factored form.

Front

What is the GCF (Greatest Common Factor) of 30x³ + 15x² - 18x - 9?

Back

The GCF is 3.

Front

How do you factor the expression 80x⁵ - 70x² - 60x⁷?

Back

10x²(8x³ - 7 - 6x⁵) is the factored form.

Front

What does it mean if (x - 3) is not a factor of 3x³ + 10x² - x - 12?

Back

It means that substituting x = 3 into the polynomial does not yield zero.

Front

What is the purpose of factoring polynomials?

Back

To simplify expressions and solve equations more easily.

Front

What is a polynomial?

Back

A mathematical expression consisting of variables, coefficients, and exponents combined using addition, subtraction, and multiplication.

Front

What is the difference between factoring and expanding?

Back

Factoring breaks down an expression into simpler components, while expanding multiplies out the components.