+321 First, we try to factor x^2 + 2x + 10. That doesn't seem quite possible, so now we try to use completing the square with (x-1)^2. We get that x^2 + 2x +10 = (x-1)^2 + 4x + 9. We can still factor it more and get (x-1)*(x-1 + 4) + 13 = (x-1)*(x+3) +13. Hence, the quotient is x+3 and the remainder is 13.
+118673 Find the quotient and remainder when x^2 + 2x + 10 is divided by x - 1.
There is more than one way to do this. My way is slightly unusual.
Normally I would just do a standard polynomial division.
f(1) = 1+2+10= 13 that is the remainder
so we have
\(f(x)=x^2+2x+10\\ f(x)=x^2+2x-3+13\\ f(x)=(x+3)(x-1)+13\\\)
Divide it by x-1 where x is not equal to 1
and we get
x+3 remainder 13
