Question

Write the HCF of the polynomials (x^2-4x+4)(x+3) and (x^2+2x-3)(x-2)?

Answer 1

first off all find the factors of given polynomial

(x^2-4x+4)(x+3)=(x-2)(x-2)(x+3)

(x^2+2x-3)(x-2)=(x^2+3x-x-3)(x-2)

=[x (x+3)-1 (x+3)][x-2]

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

so HCF=(x-2)(x+3)

Answer 2

Answer:

The HCF of the polynomials is (x-2)(x+3).

Step-by-step explanation:

First of all write the given expressions in factored form.

$(x^2-4x+4)(x+3)=(x^2-2x-2x+4)(x+3)$

$(x^2-4x+4)(x+3)=(x(x-2)-2(x-2))(x+3)$

$(x^2-4x+4)(x+3)=(x-2)(x-2)(x+3)$                 ....(1)

Similarly,

$(x^2+2x-3)(x-2)=(x^2+3x-x-3)(x-2)$

$(x^2+2x-3)(x-2)=(x(x+3)-(x+3))(x-2)$

$(x^2+2x-3)(x-2)=(x+3)(x-1)(x-2)$                ..... (2)

From (1) and (2), it is clear that the common factors are (x-2) and (x+3). So the  HCF of the polynomials is

$H.C.F.=(x-2)(x+3)$

Therefore the HCF of the polynomials is (x-2)(x+3).