(November 22, 2024) 4th block Factor by Grouping

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials with four or more terms by grouping terms in pairs and factoring out the common factors.

Front

How do you identify the greatest common factor (GCF) in a polynomial?

Back

To find the GCF, identify the highest degree of each variable in the polynomial and the largest coefficient that divides all terms.

Front

Factor the polynomial: 7r^3 - 8r^2 + 42r - 48

Back

(r^2 + 6)(7r - 8)

Front

Factor the polynomial: 8z^3 + 4z^2 - 2z - 1

Back

(4z^2 - 1)(2z + 1)

Front

What is the first step in factoring by grouping?

Back

The first step is to group the terms in pairs and factor out the common factor from each pair.

Front

Factor the polynomial: 24m^6n^3 - 36m^4n^5 + 48m^2n^6

Back

12m^2n^3(2m^4 - 3m^2n^2 + 4n^3)

Front

What does GCF stand for in polynomial factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides all terms in a polynomial.

Front

Factor the polynomial: 15a^4b - 25a^3b^2 + 35a^2b^3

Back

5a^2b(3a^2 - 5ab + 7b^2)

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials simplifies expressions and helps solve equations by breaking them down into simpler components.

Front

Factor the polynomial: 6y^3 - 9y^2 + 2y - 3

Back

(3y^2 - 1)(2y + 3)