Question

H.C.F of the 12(x^4 - x^3) and (x^4 - 3x^3 +2x^2) is option 1) x^2(x-1)(x+1)(x-2) option 2)x^2(x-1) option 3)x^2(x-2) option 4)(x-1) (x-2) any genius plz​

Answer 1

$\huge\rm\underline\purple{Solution:- }$

$\red\implies$$\tt{12 ({x}^{4} - {x}^{3} = 12 {x}^{3}(x - 1)}$

$\red\implies$$\tt{{x}^{4} - {3x}^{3} + {2x}^{2} = {x}^{2}( { x }^{2} - 3x + 2)}$

$\red\implies$$\tt{{x}^{2} (x - 1)(x - 2)}$

∴ HCF = $\small\tt{{x}^{2}(x - 1)}$

So, option 3) is the correct answer.

Hope it helps!

Answer 2

Answer:

x

2

−3x+2=x

2

−2x−x+2

x(x−2)−1(x−2)=(x−2)(x−1)

Now

x

2

−4x+3=x

2

−3x−x+3

x(x−3)−1(x−3)=(x−3)(x−1)

Thus, the only common factor is (x-1)