Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 3,2,6$ and $\mathrm { P } ( 1 ) = 20$
A) $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 12 x + 36$
B) $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 11 x + 30$
C) $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 12 x - 36$
D) $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 11 x + 30$

Question

Quizplus · Accepted Answer

Given the zeros -3, 2, and 6, the polynomial can be expressed as $P(x) = k(x + 3)(x - 2)(x - 6)$, where $k$ is a constant. Expanding this and then determining $k$ using $P(1) = 20$ leads to the polynomial $P(x) = x^3 - 5x^2 - 12x + 36$.

Find a Polynomial of Degree 3 with Real Coefficients That −3,2,6- 3,2,6−3,2,6

Find a Polynomial of Degree 3 with Real Coefficients That $- 3,2,6$