﻿

# Your Math Help is on the Way!

### More Math Help

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Factoring Polynomials

## Finding GCF (Greatest Common Factor)

•the largest natural number that divides all given numbers evenly

Find the GCF of 24 and 60

 List Factors Prime Factorization Factors of 24: 1 2 3 4 6 8 12 24 Factors of 60: 1 2 3 4 5 6 10 12 15 20 30 60

## Finding GCF Of Variables

Find the GCF of x2y3z and x3z

Consider each variable that exists in each Monomial

Therefore, GCF of x2y3z and x3z is x2*1*z = x2z

The simplest method of factoring a polynomial is to factor out
the greatest common factor (GCF) of each term.

Example: Factor 18x3 + 60x.

 GCF of 18 and 60 = 6 Determine GCF of the coefficients of each term. GCF x3 and x = x Determine GCF of the variables in each term. GCF = 6x The GCF of the polynomial is the product of the GCF’s found above Factored form GCF ->* Rewrite and Simplify within the parentheses. Check the answer by multiplication.

The simplest method of factoring a polynomial is to factor out
the greatest common factor (GCF) of each term.

Example: Factor 24x2y + 60x3

 GCF of 24 and 60 = 12 Determine GCF of the coefficients of each term. GCF x2y and x3 = x2 Determine GCF of the variables in each term. GCF = 12x2 The GCF of the polynomial is the product of the GCF’s found above. Factored form GCF -> * Rewrite and Simplify within the parentheses. Check the answer by multiplication.

The simplest method of factoring a polynomial is to factor out
the greatest common factor (GCF) of each term.

Example: Factor 4x2 -12x+ 20.

 GCF of 4, 12 and 20 = 4 Determine GCF of the coefficients of each term. GCF x2, x , 0 = N/A Determine GCF of the variables in each term. GCF = 4 The GCF of the polynomial is the product of the GCF’s found above. Factored form GCF ->* Simplify. Check the answer by multiplication.

A common binomial factor can be factored out of certain
expressions.

Example: Factor the expression 5(x + 1) – y(x + 1).
5(x + 1) – y(x + 1) = (5 – y)(x + 1)
(5 – y)(x + 1) = 5(x + 1) – y(x + 1) Check.

Some polynomials can be factored by grouping terms to produce
a common binomial factor.

Examples: 1. Factor xy + 2y + 7x + 14.

 xy + 2y + 7x + 14. = (xy + 2y) + (7x + 14). Group terms. = y(x + 2) + 7(x + 2) Factor each pair of terms. = (x + 2)(y + 7) Factor out the common binomial.

2. Factor 6x3 - 8x2 + 3xy - 4y.

 6x3 - 8x2 + 3xy - 4y. = (6x3 - 8x2)+ (3xy - 4y). Group terms. = 2x2(3x – 4) + y(3x – 4) Factor. = (2x2 + y)(3x – 4)

Some polynomials can be factored by grouping terms to produce
a common binomial factor.

Examples: 3. Factor 2xy + 3y – 4x – 6.

 2xy + 3y – 4x – 6 = (2xy + 3y) – (4x + 6) Group terms. = (2x + 3)y – (2x + 3)2 Factor each pair of terms. = (2x + 3)(y – 2) Factor out the common binomial.

4. Factor 2a2 + 3bc – 2ab – 3ac.

 2a2 + 3bc – 2ab – 3ac = 2a2 – 2ab – 3ac + 3abc Rearrange terms. = (2a2 – 2ab) – (3ac + 3bc) Group terms. = 2a(a – b) – 3c(a – b) Factor. = 2a(a – b) – 3c(a – b) Factor. = (2a – 3c)(a – b)
﻿