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Find the quotient and remainder when x^2 + 2x + 10 is divided by x - 1.

 Oct 30, 2019
 #1
avatar+236 
+2

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.

 Oct 30, 2019
 #2
avatar+105672 
+1

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

 Oct 30, 2019
edited by Melody  Oct 30, 2019

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