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

How do you determine if a binomial is a factor of a polynomial?

Back

To determine if a binomial is a factor of a polynomial, you can use polynomial long division or synthetic division. If the remainder is zero, then the binomial is a factor.

Tags

CCSS.HSA.APR.D.6

Front

What is the first step in factoring by grouping?

Back

The first step in factoring by grouping is to rearrange the polynomial into two groups that can be factored separately.

Front

What is the factored form of the polynomial 4p^3 + 8p^2 + 3p + 6?

Back

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

Front

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

Back

The factored form is (x² - 2)(x + 7).

Front

What is the significance of the common factor in factoring by grouping?

Back

The common factor allows you to simplify the polynomial into a product of simpler polynomials, making it easier to solve or analyze.

Front

How do you factor the polynomial 6n^3 + 3n^2 + 8n + 4 by grouping?

Back

Group the terms: (6n^3 + 3n^2) + (8n + 4), factor out common factors from each group, resulting in (3n^2 + 4)(2n + 1).

Front

What is the factored form of the polynomial 3x^3 - 4x^2 + 9x - 12?

Back

The factored form is (x^2 + 3)(3x - 4).

Front

What is a polynomial?

Back

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

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as (a + b) or (x - 3).