Algebrahard · Past Paper
Factorize: x^5 + x + 1
A(x^2+x+1)(x^3-x^2+1)
B(x^2-x+1)(x^3+x^2+1)
C(x^3+x+1)(x^2-x+1)
D(x^2+x+1)(x^3+x^2+1)
✓ Correct Answer: A — (x^2+x+1)(x^3-x^2+1)
Add and subtract x^2: (x^5-x^2) + (x^2+x+1) = x^2(x^3-1) + (x^2+x+1) = x^2(x-1)(x^2+x+1) + (x^2+x+1).
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