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) a^{3} + 2a^{2} – 3a and 2a^{3} + 5a^{2} – 3a2. Find the highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of the three polynomials:
(i) 3m^{2} – 7m^{2}n + 5mn^{2} – n^{3}, m^{2}n + 3mn^{2} – 3m^{3} – n^{3} and 3m^{3} + 5m^{2}n + mn^{2} – n^{3}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)
8th Grade Math Practice
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