Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zero of $- 4$ having multiplicity 2 and zero of 8 having multiplicity $1 ; P ( 0 ) = - 128$
A) $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 8 x - 128$
B) $P ( x ) = x ^ { 3 } + x ^ { 2 } - 48 x - 128$
C) $P ( x ) = x ^ { 3 } - 48 x - 128$
D) $P ( x ) = x ^ { 3 } - 48 x ^ { 2 } - 128$

Question

Quizplus · Accepted Answer

The polynomial with zeros -4 (multiplicity 2) and 8 (multiplicity 1) is $P(x) = (x + 4)^2(x - 8)$. Expanding this gives $P(x) = x^3 - 8x^2 + 16x - 128$. Evaluating at $x = 0$ gives $P(0) = -128$, which matches the condition.

Find a Polynomial of Degree 3 with Real Coefficients That −4- 4−4

Find a Polynomial of Degree 3 with Real Coefficients That $- 4$