Question

In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:
f(x) = x³ -6x²+11x-6, g(x) = x²-3x+2

Answer 1

The polynomial g(x) is a factor of polynomial f(x).

Given,

f(x) = x³ -6x²+11x-6, g(x) = x²-3x+2

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

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

∴ g(x) = (x-1) (x-2)

the values  x= 1 and x = 2 should satisfy the polynomial f(x) = x³ - 6x² + 11x - 6 if given g(x) is a factor.

Now, consider,

f(x) = x³ - 6x² + 11x - 6

f(1) = 1^3 - 6(1)^2 + 11(1) - 6 = 1 - 6 + 11 - 6 = 12 - 12 = 0

f(2) = 2^3 - 6(2)^2 + 11(2) - 6 = 8 - 24 + 22 - 6 = 30 - 30 = 0

Therefore, it's proved that the given g(x) is a factor of the polynomial f(x) = x³ -6x²+11x-6

Answer 2

Answer:

•g(x) is factor of f(x)..

•steps are given above.. please refer the pic..

•hope its helpful