# Use the Remainder Theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial. (2x^3 -5x^2 +7x+1)div (x-5)

Use the Remainder Theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial. $\left(2{x}^{3}-5{x}^{2}+7x+1\right)÷\left(x-5\right)$
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empatiji2v
If a polynomial P(x) is devided by x-r, the remainder is a constant P(r), for $\left(2{x}^{3}-5{x}^{2}+7x+1\right)÷\left(x-5\right)$ we check P(5):
$P\left(5\right)=2\left(5{\right)}^{3}-5\left(5{\right)}^{2}+7\left(5\right)+1=161\ne 0$.
Result:
The remainder is $161\ne 0,x-5$ is not a factor of the polynomial.