Learn how to solve H.C.F. of polynomials by factorization splitting the middle term.
Solved examples on highest common factor of polynomials by factorization:
1. Find out the H.C.F. of x^{2} - 3x - 18 and x^{2} + 5x + 6 by factorization.= x(x - 6) + 3(x - 6)
= (x - 6) (x + 3)
Second expression = x^{2} + 5x + 6= x(x + 3) + 2(x + 3)
= (x + 3) (x + 2)
Therefore, in the two polynomials (x + 3) is the only common factors, so, the required H.C.F. = (x + 3).
= 2 × (a + 2b) × (a - 2b)
Second expression = (4a^{2} + 4ab - 24b^{2})= 4[a(a + 3b) - 2b(a + 3b)]
= 4(a + 3b) (a - 2b)
= 2 × 2 × (a + 3b) × (a - 2b)
Third expression = (2a^{2} - 12ab + 16b^{2})= 2[a(a - 4b) - 2b(a - 4b)]
= 2(a - 4b) (a - 2b)
= 2 × (a - 4b) × (a - 2b)
From the above three expressions ‘2’ and ‘(a - 2b)’ are the common factors of the expressions.
Therefore, the required H.C.F. is 2 × (a - 2b) = 2(a - 2b)
8th Grade Math Practice
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