# Which of the Following is not a Zero of the Polynomial p(x)=x³ -11x²+36x-36?

By BYJU'S Exam Prep

Updated on: October 17th, 2023

Which of the following is not a zero of the polynomial p(x)=x³ -11x²+36x-36?

1. 2
2. 3
3. 4
4. 6

To find the solution to this problem, we will substitute each option into the polynomial p(x) and evaluate it. Any option which does not yield zero when substituted into the polynomial p(x) will not be a zero of the given polynomial p(x)=x³ -11x²+36x-36

## Which of the Following is not a Zero of the Polynomial p(x)=x³ -11x²+36x-36?

Solution:

1. Evaluate p(2)
p(2) = (2)³ – 11(2)² + 36(2) – 36
p(2) = 8 – 44 + 72 – 36 = 0
2. Evaluate p(3)
p(3) = (3)³ – 11(3)² + 36(3) – 36
p(3) = 27 – 99 + 108 – 36 = 0
3. Evaluate p(4)
p(4) = (4)³ – 11(4)² + 36(4) – 36
p(4) = 64 – 176 + 144 – 36 = -4
4. Evaluate p(6)
p(6) = (6)³ – 11(6)² + 36(6) – 36
p(6) = 216 – 396 + 216 – 36 = 0

Based on the evaluations, we find that:

p(2) = 0

p(3) = 0

p(4) = -4

p(6) = 0

Among the given options, only Option c (4) does not yield zero when substituted into the polynomial p(x). Therefore, Option c (4) is the answer, and it is not a zero of the polynomial p(x) = x³ – 11x² + 36x – 36.