Problem

2) Let \( P(x)=x^{4}+5 x^{3}+4 x^{2}-3 x+9 \).
a) Compute \( P(-3) \).
b) Decompose P into irreducible factors.

Answer

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Answer

P(x) = (x+3)(x^3+2x^2-x+3)

Steps

Step 1 ：P(-3) = (-3)^{4}+5(-3)^{3}+4(-3)^{2}-3(-3)+9

Step 2 ：P(-3) = 81-135+36+9+9

Step 3 ：P(-3) = 0

Step 4 ：P(x) = (x+3)(x^3+2x^2-x+3)

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