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 x2 - 3x - 18 and x2 + 5x + 6 by factorization.
= x(x - 6) + 3(x - 6)
= (x - 6) (x + 3)Second expression = x2 + 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. Find out the H.C.F. of (2a2 - 8b2), (4a2 + 4ab - 24b2) and (2a2 - 12ab + 16b2) by factorization.
= 2 × (a + 2b) × (a - 2b)Second expression = (4a2 + 4ab - 24b2)
= 4[a(a + 3b) - 2b(a + 3b)]
= 4(a + 3b) (a - 2b)
= 2 × 2 × (a + 3b) × (a - 2b)Third expression = (2a2 - 12ab + 16b2)
= 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
From H.C.F. of Polynomials by Factorization to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
New! CommentsHave your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.