Thread: Find a polynomial of degree 3 with real coefficients that satisfies...

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.?

Zeros of -3,-1, 4, and P(2) = 5

I am attempting this problem in order to study for an upcoming test. I am stuck on this one, and would really like to learn if someone could please assist me, I would very much appreciate it.

I have multiplied (x + 3)(x+1)(x-4)
to get x^3 - 13x -12
Where do I go from here?

Originally Posted by SammyAbby

I have multiplied (x + 3)(x+1)(x-4)
to get x^3 - 13x -12
Where do I go from here?

P(x) = k(x+3)(x+1)(x-4)

5 = k(2+3)(2+1)(2-5)

solve for k

Thank you for your assistance...I am still a bit confused...my book says that the answer is P(x) = (-x^3/6) + (13x/6) + 2

How did they get this?