Question

16.
A
The H.C.F. of (x + 3x2 - x - 3) and
(x3 + 4x2 + x-6) is :
(A) x-1.
(B) x +2
(C) x+3
(D) x² + 2x - 3​

Answer 1

Answer:

b

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Answer 2

The HCF of multiple polynomials can be found out by factorizing them.

Now, observe the first polynomial f(x) = x^2+x-2.

Clearly f(1) = 1+1–2 = 0. Hence (x-1) is a factor of this polynomial.

[If ‘a’ is a factor of a polynomial f(x), then (x-a) is a factor of f(x)]

Further, the polynomial can be written as f(x) = (x-1)*(x+2).

Now the second polynomial is g(x) = x^3+4x^2+x-6

Again , this is divisible by (x-1) as g(x) = 1+4+1–6 = 0.

g(x) can be written as (x-1) * (x^2 + 5x + 6), which can be further written as

g(x) = (x-1)* (x+2) * (x+3)

Hence,

f(x) = (x-1)*(x+2)

g(x) = (x-1)* (x+2) * (x+3)

Clearly, the HCF of f(x) and g(x) is (x-1).

Hope this will help you.