For the​ following, find the function P defined by a polynomial of degree 3 with real coefficients that satisfy the given conditions.

Question

For the​ following, find the function P defined by a polynomial of degree 3 with real coefficients that satisfy the given conditions.

The zeros are -3,-1, and 4

P(-2)=12

P(x)=

(simplify your answer)

Answer 1

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

P(-2)=12 = a(1)(-1)(-6)=6a

12=6a

a=12/6= 2

P(x)= 2(x+3)(x+1)(x-4) in intercept form

=2(x^2+4x+3)(x-4)=2(x^3-13x-12)

P(x)= 2x^3 -26x-24 in standard form

check the answer, plug in each zero

P(-1) = -2+26-24 = 0

P(-3) = -54+78-24=0

P(4)= 128-104-24=0