Question

examine wheather (x+2) is a factor of x^4+3x^3+3x^2+x+1

Answer 1

Hola Mate!!

Here's your answer:-

$g(x) = 0 \\ = > x + 2 = 0 \\ = > x = - 2 \\ \\ p(x) = {x}^{4} + 3 {x}^{3} + 3 {x}^{2} + x + 1 \\ = > p( - 2) = { ( - 2)}^{4} + 3 \times { (- 2)}^{3} + 3 \times {( - 2)}^{2} + ( - 2) + 1 \\ = 16 + 3 \times - 8 + 3 \times 4 - 2 + 1 \\ = 16 - 24 + 12 - 1 \\ = 3$
g(x) is not equal to 0. So, it is not a factor of p(x).

Hope it helps
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