# Factoring Polynomials Calculator

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In simple words, factoring polynomials is the opposite of multiplication of polynomials.  When we factor a polynomial , one will be looking for a simpler polynomial that can be multiplied together to give back the original polynomial which we started with.

## Step by step Factoring Polynomials

Factoring polynomial is somewhat similar to factoring the numbers. While factoring we find the numbers or polynomials that divide evenly from original numbers or polynomials. While factoring the polynomials we find the factors consisting of numbers as well as variables.
Suppose we have the simplified polynomial obtained by distributing the parentheses.

Example: $2( x-3)$  = $2x- 6$
Factoring this polynomial would be reverse of distributing. Here we take common factor out and put it out of the parentheses.

$2x -6$ = $2(x) -2(3)$
= $2(x-3)$

We can factorize a polynomial by applying different methods.

### Factorization by Common Factor

Steps to be followed for factorizing a polynomial  by taking out common factor.

I .Write each term as product of prime factors
II. Separate the common factors
III. Combine remaining terms and apply reverse of distributive law.

Binomial as a common factor in the polynomial.

### Factorization by Grouping

If all the terms of the given polynomial do not have common factor then factorization by grouping is applied. The terms are rearranged in a way so as to form the groups with common factor.

It should be noted that grouping randomly won’t always give proper factors. Care should be taken to form groups properly.

$x^{3} + 3x^{3} + 8x + 24$

Here there are no common factors to all the four terms. Let us try to factorize by grouping. Let us make group of first two terms and another group of last two terms.

$(x^{3} + 3x^{3} ) + ( 8x + 24 )$

Get common factor out of each group.

= $x^{2}( x + 3 )+8(x+3)$

Here x + 3 can be taken out as common factor.
= $(x^{2}+ 8 ) ( 3 + x )$

## Examples of Factoring Polynomials

### Solved Examples

Question 1: Factorize 4a -16b
Solution:

Write each term as product of factors
$4a = 4 \times a$
$16b = 4 \times 4 \times b$

Here the common factor is $4$.
Take $4$ out
$4a - 16b$ = $4(a) - 4(4b)$
= $4(a - 4b)$

Question 2: Factorize : 42a2  -  28 a2b + 14a2b2
Solution:

Write each term as product of prime  factors.

42a2 = $2 \times 3 \times 7 \times a \times a$
28a2b = $2 \times 2 \times 7 \times a \times a \times b$
14a2b2  = $2 \times 7 \times a \times a \times b \times b$

Check the greatest common factor

GCF = $2\times 7\times a\times a$ = 14a2
42a2  =14a2 $\times$ 3
28a2b = 14a2  $\times$ (2b)
14a2b2 =14a2 $\times$ (b2)

42a2  -  28 a2b + 14a2b2
=14a2 $\times (3)$  -14a2 $\times$ (2b) + 14a2 $\times$ (b2)

Take out the common factor and put other terms inside the parentheses.

=14a2  (3 - 2b + b2)