Answer:
2(x + 3)(x + 1)(x - 4)
or 2x^3 - 26x - 24.
Step-by-step explanation:
We can write the polynomial if factor form:
P(x) = a(x + 3)(x + 1)(x - 4) where a is some constant.
Now, since f(-2) = 12 we can write :
12 = a(-2 + 3)(-2 + 1)(-2-4)
12 = 6a
a = 2.
So the polynomial is
2(x + 3)(x + 1)(x - 4).
Expanded that is
2(x + 3)(x^2 - 3x - 4)
= 2(x^3 - 3x^2 - 4x + 3x^2 - 9x - 12)
= 2x^3 - 26x - 24.
The polynomial of degree 3 with real coefficients and zeros of -3, -1, and 4 is x³+x²-9x-9
If a polynomial has real coefficients and zeros of -3, -1, and 4, the factors of the polynomial will be expressed as:
(x + 3), (x+1) and (x-3)
Taking the product of the polynomials;
P(x) = (x+3)(x-3)(x+1)
P(x) = (x² - 9)(x+1)
P(x)= x³+x²-9x-9
Hence the polynomial of degree 3 with real coefficients and zeros of -3, -1, and 4 is x³+x²-9x-9
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