Question

verify if -2 and 3 are zeroes of the polynomial 2x^3 -3x^2-11x +6 . if yes factorize the polynomial

Answer 1

Answer:

Yes , (-2) and 3 are the zeroes of the polynomial p(x) = 2x^3-3x^2-11x+6

And the Factorized Form of 2x^3-3x^2-11x+6 = (x+2)(2x-1)(x-3)

Step-by-step explanation:

(-2) and 3 are zeroes of the polynomial only if the solution of polynomial after putting the value of "x" is 0

Let p(x) = 2x^3-3x^2-11x+6

p(-2) = 2(-2)^3-3(-2)^2-11(-2)+6 = -16-12+22+6 = -28+28 = 0

p(3) = 2(3)^3-3(3)^2-11(3)+6 = 54-27-33+6 = 54-60+6 = 54-54 = 0

.

Hence, Both (-2) and 3 are the zeroes of the polynomial p(x)=2x^3-3x^2-11x+6

Now, Since (-2) is a zero of the polynomial. Therefore, The 1st factor is (x+2)

=> 2x^2(x+2)-7x(x+2)+3(x+2) = (x+2)(2x^2-7x+3) = (x+2)(2x^2-6x-x+3)

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

THEREFORE, THE FACTORIZED FORM IS :- (x+2)(2x-1)(x-3)