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:

First expression = x

= x

= x(x - 6) + 3(x - 6)

= (x - 6) (x + 3)

Second expression = x= x

= 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).

First expression = (2a

= 2(a

= 2[(a)

= 2(a + 2b) (a - 2b), we know a

= 2 × (a + 2b) × (a - 2b)

Second expression = (4a= 4(a

= 4(a

= 4[a(a + 3b) - 2b(a + 3b)]

= 4(a + 3b) (a - 2b)

= 2 × 2 × (a + 3b) × (a - 2b)

Third expression = (2a= 2(a

= 2(a

= 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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