# 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.

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)