Factor by Grouping

Front

What is factoring by grouping?

Back

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

Front

What is a polynomial?

Back

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

Front

What does it mean for (x-3) to be a factor of a polynomial?

Back

It means that when the polynomial is divided by (x-3), the remainder is zero.

Front

How do you factor the expression x³ - 4x² - 4x + 16?

Back

The factored form is (x-4)(x²-4).

Front

What is the first step in factoring by grouping?

Back

The first step is to group the terms of the polynomial into pairs.

Front

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

Back

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

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials helps simplify expressions and solve equations.

Front

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

Back

The factored form is (5n² + 3)(n - 2).

Front

What does it mean if a polynomial is not factorable?

Back

It means that the polynomial cannot be expressed as a product of simpler polynomials.

Front

What is the significance of the zero product property in factoring?

Back

The zero product property states that if the product of two factors is zero, at least one of the factors must be zero.