Find the function P defined by a polynomial of degree 3 with real coefficients that satisfy the given conditions.

Question

The zeros are -3,-1, and 4. The leading coefficient is -6.

what is it in standard form?

Answer 1

The expression for the polynomial is a product of following factors:

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

(x - 4)( x² + 4x +3) =

x³ -13x - 12

x³ - 13x - 12 ← multiply by "-6"

-6x³ + 78x + 72

Answer 2

When they give you the zeros, use the factored form of the polynomial. Since it's degree three, there are three factors:

P(x) = a·(x-p)·(x-q)·(x-r)

where a is the leading coefficient, and p, q, and r are the zeros. Plug the given values into the factored form, then multiply it out and arrange it in order of decreasing powers of x (standard form), P(x) = ax³ + bx² + cx + d.