Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 2,1,0$ and $P ( 2 ) = 40$
A) $P ( x ) = 5 x ^ { 2 } + 5 x - 10$
B) $P ( x ) = 5 x ^ { 3 } - 5 x ^ { 2 } - 10 x$
C) $P ( x ) = 5 x ^ { 3 } + 15 x ^ { 2 } - 10 x$
D) $P ( x ) = 5 x ^ { 3 } + 5 x ^ { 2 } - 10 x$

Question

Quizplus · Accepted Answer

Since the zeros are -2, 1, and 0, the polynomial can be written as:$$P(x) = a(x + 2)(x - 1)(x - 0)$$$$P(x) = a(x^2 + x - 2x - 2)(x)$$$$P(x) = a(x^2 - x - 2x - 2)(x)$$$$P(x) = a(x^3 - x^2 - 2x^2 - 2x)$$$$P(x) = a(x^3 - 3x^2 - 2x)$$To find the value of a, we can use the given condition P(2) = 40:$$P(2) = a(2^3 - 3(2)^2 - 2(2)) = 40$$$$a(8 - 12 - 4) = 40$$$$a(-8) = 40$$$$a = -5$$Therefore, the polynomial is:$$P(x) = -5(x^3 - 3x^2 - 2x)$$$$P(x) = -5x^3 + 15x^2 + 10x$$

Find a Polynomial of Degree 3 with Real Coefficients That −2,1,0- 2,1,0−2,1,0

Find a Polynomial of Degree 3 with Real Coefficients That $- 2,1,0$