Question

Kiran thinks he knows one of the linear factors of p(x)=x^3+x^2-17x+15. After finding that p(3)=0, Kiran suspects that x-3 is a factor of p(x, so he sets up a diagram to check. Here is the diagram he made to check his reasoning, but he set it up incorrectly

Answer 1

To check if x-3 is a factor of the polynomial p(x), divide p(x) by x-3 using long division or synthetic division. If the remainder is zero, then x-3 is indeed a factor.

Kiran suspects that x-3 is a factor of the cubic polynomial
`p(x)=x^3+x^2-17x+15` because p(3) = 0. To check his reasoning, he sets up a diagram. However, the given diagram is incorrect and does not show the correct setup.

To check if x-3 is a factor of p(x), we need to divide p(x) by x-3 using long division or synthetic division. If the remainder is zero, then x-3 is indeed a factor.

Once the correct setup is determined and the division is carried out, if the remainder is zero, then Kiran's suspicion is correct and x-3 is a factor of p(x). Below may be the diagram of the question