Subscribe to our YouTube channel for the latest videos, updates, and tips.


Highest Common Factor of Polynomials by Factorization

How to find the highest common factor of polynomials by factorization?

Let us follow the following examples to know how to find the highest common factor (H.C.F.) or greatest common factor (G.C.F.) of polynomials by factorization.


Solved examples of highest common factor of polynomials by factorization:

1. Find out the H.C.F. of a2b + ab2 and a2c + abc by factorization.

Solution:

First expression = a2b + ab2

                      = ab(a + b)

                      = a × b × (a + b)


Second expression = a2c + abc

                          = ac(a + b)

                          = a × c × (a + b)

It can be seen, in both the expressions ‘a’ and ‘(a + b)’ are the common factors and there is no other common factor.

Therefore, the required H.C.F. a2b + ab2 and a2c + abc is a(a + b)



2. Find the out the H.C.F. of (a2b + a2c) and (ab + ac)2 by factorization.

Solution:

First expression = a2b + a2c

                      = a2(b + c)

                      = a × a × (b + c)

Second expression = (ab + ac)2

                          = (ab + ac) (ab + ac)

                          = a(b + c) a(b + c)

                          = a × a × (b + c) × (b + c)    

It can be seen that, in both the expressions ‘a’, ‘a’ and ‘(b + c)’ are the common factors and there is no other common factor.

Therefore, the required H.C.F. is a × a × (b + c) = a2(b + c).



3. Find the out the H.C.F. of c(a + b)2, (a2c2 – b2c2) and a(ac2 + bc2) by factorization.

Solution:

First expression = c(a + b)2

                      = c × (a + b) × (a + b)

Second expression = (a2c2 - b2c2)

                          = c2(a2 - b2)

                          = c2(a + b) (a - b)

                          = c × c × (a + b) × (a - b)

Third expression = a(ac2 + bc2)

                       = ac2(a + b)

                       = a × c × c × (a + b)

It can be seen that, c and (a + b) are the common factors of the expressions.

Therefore, the required H.C.F. of c(a + b)2, (a2c2 – b2c2) and a(ac2 + bc2) is c(a + b)



4. Find out the H.C.F. of 3x2(y + z)2 and 6x(y2 - z2) by factorization.

Solution:

First expression = 3x2(y + z)2

                      = 3x2 (y + z)(y + z)

                      = 3 × x × x × (y + z) × (y + z)

Second expression = 6x(y2 - z2)

                          = 6x(y2 - z2)

                          = 6x(y + z) (y - z)

                          = 2 × 3 × x × (y + z) × (y - z)

Therefore, the required H.C.F. is 3 × x × (y + z) = 3x(y + z)






8th Grade Math Practice

From Highest Common Factor of Polynomials by Factorization to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Simple Interest | Word problem on Simple Interest | Free

    Jun 19, 25 02:54 AM

    Worksheet on Simple Interest 2
    In worksheet on simple interest we will get different types of question on calculating the simple interest, the principal amount, the rate of interest and the word problems on simple interest.

    Read More

  2. Terms Related to Simple Interest | Simple Interest Formula | Principal

    Jun 19, 25 12:20 AM

    Terms Related to Simple Interest
    In terms related to simple interest we will learn all the terms related to simple interest. The terms related to simple interest are Interest, Principal, Amount, Simple Interest, Time or period of tim…

    Read More

  3. Introduction to Simple Interest | Definition | Formula | Examples

    Jun 18, 25 01:50 AM

    Simple Interest
    In simple interest we will learn and identify about the terms like Principal, Time, Rate, Amount, etc. PRINCIPAL (P): The money you deposit or put in the bank is called the PRINCIPAL.

    Read More

  4. 5th Grade Profit and Loss Percentage Worksheet | Profit and Loss | Ans

    Jun 18, 25 01:33 AM

    5th Grade Profit and Loss Percentage Worksheet
    In 5th grade profit and loss percentage worksheet you will get different types of problems on finding the profit or loss percentage when cost price and selling price are given, finding the selling pri…

    Read More

  5. Worksheet on Profit and Loss | Word Problem on Profit and Loss | Math

    Jun 18, 25 01:29 AM

    Worksheet on Profit and Loss
    In worksheet on profit and loss, we can see below there are some different types of questions which we can practice in our homework.

    Read More