Question

find the product
x 4 + x3 + x 2 +1 and x-1​

Answer 1

$\huge\mathbb{\fcolorbox{purple}{pink}{answer}}$

$g(x) = x - 1$

$g(x) = x - 1 = 0$

$g(x) = 1$

$p(x) = {x}^{4} + {x}^{3} + {x}^{2} + 1$

$p(1) = {(1)}^{4} + {(1)}^{3} + {(1)}^{2} + 1$

$p(1) = 1 + 1 + 1 + 1$

$p(1) = 4$

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Answer 2

$\sf{\underline{\underline{\huge{\mathbb{SOLUTION}}}}}$

$\sf\implies ( x - 1 ) ( x^4 +x^3 + x^2 + 1 )$

$\sf\implies x ( x^4 + x^3 +x^2 + 1 ) - 1 ( x^4 + x^3 + x^2 + 1 )$

$\sf\implies x^5 + x^4 + x^3 + x - x^4 - x^3 - x^2 - 1$

$\sf\implies x^5 + x - x^2 - 1$

$\sf\implies x^5 - x^2 + x - 1$