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The relation between H.C.F. and L.C.M. of two polynomials is the product of the two polynomials is equal to the product of their H.C.F. and L.C.M.
If p(x) and q(x) are two polynomials, then p(x) β q(x) = {H.C.F. of p(x) and q(x)} x {L.C.M. of p(x) and q(x)}.
= a(a β 7) β 1(a β 7)
= (a β 7) (a β 1)
Therefore, the H.C.F. = (a β 7) and L.C.M. = (a β 7) (a β 5) (a β 1)
Note:
(i) The product of the two expressions is equal to the product of their factors.
(ii) The product of the two expressions is equal to the product of their H.C.F. and L.C.M.
Product of the two expressions = (a2 β 12a + 35) (a2 β 8a + 7)= (a β 7) (a β 5) (a β 7) (a β 1)
= (a β 7) (a β 7) (a β 5) (a β 1)
= H.C.F. Γ L.C.M. of the two expressions
= a(a + 9) + 1(a + 9)
= (a + 9) (a + 1)
Therefore, the H.C.F. = (a + 9)
Therefore, L.C.M. = Product of the two expressions/H.C.F.
= (a2+7aβ18)(a2+10a+9)(a+9)
= (a+9)(aβ2)(a+9)(a+1)(a+9)
= (a β 2) (a + 9) (a + 1)
Solution:
According to the problem,
Required Expression = L.C.M.ΓH.C.F.Givenexpression
= (m3β10m2+11x+70)(xβ7)x2β5xβ14
= (m2β5mβ14)(xβ5)(xβ7)x2β5xβ14
8th Grade Math Practice
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