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


Worksheet on H.C.F. of Polynomials

Practice the worksheet on H.C.F. of polynomials. The questions are based on finding the highest common factor of two or more polynomials.

We know, to find the highest common factor (H.C.F.) of two or more than two polynomials is the polynomial of highest measures (or dimensions) which divides each of the polynomials without remainder.

For example: The highest common factor of 4am3 and 2am3 + 4a2m2

It will be easy to pick out the common factors if the polynomials are arranged as follows;

4am3 = 4am3

2am3 + 4a2m2 = 2am2(m + 2a); [taking the common factor 2am^2 from both the terms].

Therefore, the H.C.F. of 4am3 and 2am3 + 4a2m2 = 2am2


1. Find the highest common factor (H.C.F.) of the two polynomials:

(i) x2 + xy and x2 – y2

(ii) (p + q)2 and p2 – q2

(iii) 2m2 – 2mn and m3 – m2n

(iv) a4 + a3b and a3 + b3

(v) 6p2 – 9pq and 4p2 – 9q2

(vi) p2 – p – 20 and p2 – 9p + 20

(vii) 2k2 – k – 1 and 3k2 – k - 2

(viii) z2 + 3z + 2 and z2 - 4

(ix) w2 – 18w + 45 and w2 - 9

(x) ab – b and a4b - ab


2. Find the highest common factor (H.C.F.) of the three polynomials:

(i) a3 – a2m, a3 – am2 and a4 – am3

(ii) k2 – x2, k2 – kx and k2x – kx2

(iii) a2 + a, (a + 1)2 and a3 + 1

(iv) 2m2 + 9m + 4, 2m2 + 11m + 5 and 2m2 - 3m - 2

(v) 3y4 + 8y3 + 4y2, 3y5 + 11y4 + 6y3 and 3y4 – 16y3 – 12y3

 

Answers for the worksheet on H.C.F. of polynomials are given below to check the exact answers of the above questions.


Answers:


1. (i) x + y

(ii) p + q

(iii) m(m – n)

(iv) a + b

(v) 2p – 3q

(vi) p - 5

(vii) k - 1

(viii) z + 2

(ix) w - 3

(x) b(a – 1)


2. (i) a(a – m)

(ii) k - x

(iii) a + 1

(iv) 2m + 1

(v) y2(3y + 2)







Math Homework Sheets

8th Grade Math Practice

From Worksheet on H.C.F. of Polynomials 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

RSS

  1. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  2. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More