use the remainder theorem to find the remainder when p(x)=x^4+9x^3+2x^2-x+5 is divided by x-2 show you steps
To find the remainder when dividing the polynomial p(x)=x^4+9x^3+2x^2-x+5 by x-2, we can use the remainder theorem.
According to the remainder theorem, if we divide a polynomial p(x) by x-a, the remainder is given by evaluating p(a).
In this case, we want to divide p(x) by x-2. Therefore, we need to find p(2) to determine the remainder.
Substituting x=2 into p(x), we have:
p(2) = (2)^4 + 9(2)^3 + 2(2)^2 - 2 + 5
= 16 + 9(8) + 2(4) -2 + 5
= 16 + 72 + 8 - 2 + 5
= 99
Therefore, the remainder when p(x) is divided by x-2 is 99.