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Given that (x+1) is a factor of f(x) = x3 + 4x2 + 5x + c.

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1. (i) Given that (x+1)(x+1) is a factor of f(x)=x3+4x2+5x+cf(x) = x^3 + 4x^2 + 5x + c.

a) Find the value of cc.

Step 1: By the Factor Theorem, if (x+1)(x+1) is a factor, then f(−1)=0f(-1) = 0.

f(−1)=(−1)3+4(−1)2+5(−1)+cf(-1) = (-1)^3 + 4(-1)^2 + 5(-1) + c 0=−1+4(1)−5+c0 = -1 + 4(1) - 5 + c 0=−1+4−5+c0 = -1 + 4 - 5 + c
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