x²+3x+2 divided by x+2 NEED TO SEE WORK PLEASE

Question

anonymous · Answer

x²+3x+2 divided by x+2 =x+1

whpalmer4 · Answer

To do polynomial long division of the dividend (here $x^2+3x+2$) by a divisor (here $x+2$), first divide the highest exponent term of the dividend by the highest exponent term of the divisor.

$x^2/x = x$, so the first term of our quotient is $x$.  Now we multiply that first term of the quotient by the entire divisor, write that below our problem, and subtract:
                      x
       ---------------
x+2 |  x^2 + 3x + 2
       - (x^2 + 2x)
       -------------
           0x^2 + x + 2

Now we divide the first term of the remaining portion by the first term of the divisor and repeat the process.  $x/x = 1$ so the next term of the quotient is $1$:

                      x  + 1
       ---------------
x+2 |  x^2 + 3x + 2
       - (x^2 + 2x)
       -------------
           0x^2 + x + 2
                  - (  x + 2)
                 ----------
                               0

the remaining portion is 0, so we have no remainder, and our quotient is $x+1$.

Check the result by multiplying the quotient by the divisor and verifying that we get the dividend back:

$$(x+2)(x+1) = x(x+1) + 2(x+1) = x^2 + x + 2x + 2 $$$$\qquad= x^2 + 3x + 2\checkmark$$