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For what value of n is the polynomial x^3 - 9x^2 + nx - 12 divisible by x - 3? Show work.

For what value of n is the polynomial x^3 - 9x^2 + nx - 12 divisible by x - 3? Show-example-1

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2 votes

Answer:

B

Explanation:

if a polynomial f(x) is divisible by (x - a) , then f(a) = 0

for the polynomial to be divisible by (x - 3) then the polynomial will equal zero when x = 3 , that is

3³ - 9(3)² + 3n - 12 = 0

27 - 9(9) + 3n - 12 = 0

27 - 81 + 3n - 12 = 0

3n - 66 = 0 ( add 66 to both sides )

3n = 66 ( divide both sides by 3 )

n = 22

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