The correct answer is:
x²-3x-4 -[tex] \frac{3}{x-2} [/tex].
Explanation:
To divide these polynomials, the dividend, x³-5x²+2x+5, goes under the box, and the divisor, x-2, goes outside of the box.
We first want to find what we multiply x by to make x³; x*x²=x³, so we write x² over -5x² in the box.
Now we multiply our divisor, x-2, by x²:
x*x²=x³
-2*x²=-2x².
This goes under x³-5x² in the box.
Now we subtract:
(x³-5x²)-(x³-2x²)=-3x².
This goes below the 2x² we wrote, and we bring down 2x.
Now we see what we multiply x by to make -3x²;
x*-3x=-3x², so we write -3x beside x² in the quotient (at the top).
We multiply our divisor, x-2, by -3x:
x*-3x=-3x²
-2*-3x=6x.
We write -3x²+6x under our -3x²+2x and subtract:
(-3x²+2x)-(-3x²+6x)=-4x.
Write this below 6x. Bring down +5.
Now we see what we multiply x by to make -4x;
x*-4=-4x, so write -4 beside -3x in the quotient.
Multiply our divisor, x-2, by -4:
x*-4=-4x;
-2*-4=8;
write -4x+8 below -4x+5 and subtract:
(-4x+5)-(-4x+8)=-3.
This gives us the quotient x²-3x-4 with a remainder of -3, so we write our full answer as x²-3x-4-(3/x-2).
