Algebra and Applications Test 2

Question : 38 of 40

Marks: +1, -0

For what value of n will the expression

3z ^3 + nz^2 + 4z - 4n

be divisible by

(z + 2)

Solution:

Let

f(z) = 3z^2 + nz^2 + 4z - 4n

is divisible by z + 2, if f(-2) = 0

⇒ 3(-2)^2 + n(-2)^2 + 4(-2) - 4n = 0

⇒ -24 + 4n - 8 - 4n = 0

From the above it is clear that f(z) is divisible by (z + 2) for any value of n.

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