Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
Zero of -2 having multiplicity 2 and zero of 4 having multiplicity 1 ; P(0)=-16
A) $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 8 x - 16$
B) $P ( x ) = x ^ { 3 } - 12 x - 16$
C) $P ( x ) = x ^ { 3 } - 12 x ^ { 2 } - 16$
D) $P ( x ) = x ^ { 3 } + x ^ { 2 } - 12 x - 16$

Question

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
Zero of  -2  having multiplicity 2 and zero of 4 having multiplicity  1 ; P(0)=-16 
A) $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 8 x - 16$
B) $P ( x ) = x ^ { 3 } - 12 x - 16$
C) $P ( x ) = x ^ { 3 } - 12 x ^ { 2 } - 16$
D) $P ( x ) = x ^ { 3 } + x ^ { 2 } - 12 x - 16$

Quizplus · Accepted Answer

The polynomial can be expressed as $P(x) = a(x + 2)^2(x - 4)$. Given $P(0) = -16$, solve for $a$: $-16 = a(0 + 2)^2(0 - 4)$, which gives $a = 1$. Thus, $P(x) = (x + 2)^2(x - 4) = x^3 - 12x - 16$.

Find a Polynomial of Degree 3 with Real Coefficients That P(x)=x3−2x2−8x−16P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 8 x - 16P(x)=x3−2x2−8x−16

Find a Polynomial of Degree 3 with Real Coefficients That $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 8 x - 16$