Question

Check whether 3x-7 is a factor of polynomial 6x3 + x2 -26x-25 .

Answer 1

Given,

• 3x-7 is a factor of the polynomial $6x^3+x^2-26x-25$.

To find,

• We have to find whether 3x-7 is a factor of the polynomial $6x^3+x^2-26x-25$ or not.

Solution,

We can simply find whether 3x-7 is a factor of the polynomial $6x^3+x^2-26x-25$ or not by substituting the given 3x-7 in the polynomial.

        3x-7 = 0

            3x = 7

              x = 7/3

Now, substitute x = 7/3 in the polynomial $6x^3+x^2-26x-25$.

p(x) =  $6x^3+x^2-26x-25$.

p(7/3) = 6(7/3)³ +(6/7)²-26(7/3) -25

          = 6(343/27) +36/49 -182/3 -25

          = 686/9 +36/49 -182/3 -25

          = 76.23 +0.73 - 60.67 -25

          = 76.96 - 85.67

          ≠0

Since the answer is not 0, then 7/3 is not a factor of the polynomial  $6x^3+x^2-26x-25$.

Hence, 3x-7 is not a factor of the polynomial $6x^3+x^2-26x-25$.