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

  1. Worksheet on Word Problems on Fractions | Fraction Word Problems | Ans

    Jul 16, 24 02:20 AM

    In worksheet on word problems on fractions we will solve different types of word problems on multiplication of fractions, word problems on division of fractions etc... 1. How many one-fifths

    Read More

  2. Word Problems on Fraction | Math Fraction Word Problems |Fraction Math

    Jul 16, 24 01:36 AM

    In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

    Read More

  3. Worksheet on Add and Subtract Fractions | Word Problems | Fractions

    Jul 16, 24 12:17 AM

    Worksheet on Add and Subtract Fractions
    Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtractio…

    Read More

  4. Comparison of Like Fractions | Comparing Fractions | Like Fractions

    Jul 15, 24 03:22 PM

    Comparison of Like Fractions
    Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example \(\frac{7}{13}\) > \(\frac{2…

    Read More

  5. Worksheet on Reducing Fraction | Simplifying Fractions | Lowest Form

    Jul 15, 24 03:17 PM

    Worksheet on Reducing Fraction
    Practice the questions given in the math worksheet on reducing fraction to the lowest terms by using division. Fractional numbers are given in the questions to reduce to its lowest term.

    Read More