Question

Omar wanted to know if x−5 is a factor of the polynomial p(x)=x3−6x2−x+30. He applied the Factor Theorem and concluded that x−5 is a factor of p(x), as shown in the following work.

Step 1: p(5)=53−6(52)−5+30
Step 2: p(5)=125−150−5+30=0
Step 3: p(5)=0, so the remainder is 0.
Step 4: The remainder is 0, so x−5 is a factor of p(x).

Did Omar make a mistake? If so, in which step does his mistake occur?

Yes, Omar's mistake is in Step 1.
Yes, Omar's mistake is in Step 3.
Yes, Omar's mistake is in Step 2.
Yes, Omar's mistake is in Step 4.
No, Omar did not make any mistakes.

Answer 1

Step 1: p(5)=53−6(52)−5+30 makes no sense
where did those numbers come from?

Step 2: p(5)=125−150−5+30=0
Step 3: p(5)=0, so the remainder is 0.
Step 4: The remainder is 0, so x−5 is a factor of p(x).

those lines were correct.

Answer 2

He means 5^3 and 5^2, not 53 and 52

Answer 3

No, Omar did not make any mistakes.