Worksheet on H.C.F. and L.C.M. of Polynomials

Practice the questions given in the worksheet on H.C.F. and L.C.M. of polynomials. The questions are based on finding the highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of two or more than two polynomials.

1. Find the highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of the two polynomials:

(i) a³ + 2a² – 3a and 2a³ + 5a² – 3a

(ii) 4u² – 9v² and 2u² – 3uv

(iii) (4u² – 25v²) and (6u² + 15uv)

(iv) m² + 9m + 20 and m² + 13m + 36

(v) k² + 2k – 15 and k² + (26/5)k + 1

2. Find the highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of the three polynomials:

(i) 3m² – 7m²n + 5mn² – n³, m²n + 3mn² – 3m³ – n³ and 3m³ + 5m²n + mn² – n³

(ii) a² – 5a + 6, a² – 4 and a³ – 3a - 2

(iii) t² + 3t – 4, t² + 5t + 4 and t² – 1

(iv) p² + 8p + 12, p² + 2p – 24 and p² + 15p + 54

(v) d² + 15d + 56, d² + 5d – 24 and d² + 8d



3. Find the lowest common multiple of xy(k² + 1) + k(x² + y²) and xy(k² – 1) + k(x² – y²).

4. Find the L.C.M. of pq – np, pq – mq, q² – 3nq + 2n², pq – 2np – mq + 2mn and pq – np – mq + mn.

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

Answers:

1. (i) H.C.F = a(a + 3)

L.C.M. = a(a – 1) (a + 3) (2a – 1)

(ii) H.C.F = 2u – 3v

L.C.M. = u(2u + 3v)(2u – 3v)

(iii) H.C.F = 2u + 5v

L.C.M. = 3u(2u + 5v) (2u – 5v)

(iv) H.C.F = m + 4

L.C.M. = (m + 4) (m + 5) (m + 9)

(v) H.C.F = k + 5

L.C.M. = (k + 5) (k – 3) (k + 1/5)

2. (i) H.C.F = 3m - n

L.C.M. = (3m – n) (m + n)² ( - n)²

(ii) H.C.F = a - 2

L.C.M. = (a + 1)² (a + 2) (a – 2) (a – 3)

(iii) H.C.F = 1

L.C.M. = (t + 4) (t + 1) (t - 1)

(iv) H.C.F = p + 6

L.C.M. = (p + 2) (p + 6) (p + 9) (p - 4)

(v) H.C.F = d + 8

L.C.M. = d(d + 8) (d + 7) (d - 3)

3. (kx + y) (kx – y) (ky + x) 

4. pq(p – m) (q – n) (q – 2n)

Math Homework Sheets

8th Grade Math Practice

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