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)