Solve the Division of Polynomials:
P(x) = x5 + 2x3 − x − 8
Q(x) = x2 − 2x + 1
P(x) : Q(x)
On the left, place the dividend. If the polynomial is not complete, leave gaps in the places that correspond.
On the right, place the divisor in a box.
Divide the first monomial of the dividend by the first monomial of the divisor and put it below the box of the divisor.
x5 : x2 = x3
Multiply each term of the polynomial divisor by the previous result and subtract the dividend polynomial:
Divide the first monomial of the dividend again by the first monomial of the divisor. Then, multiply the result by the divisor and subtract the dividend.
2x4 : x2 = 2 x2
Proceed as before.
5x3 : x2 = 5 x
Again, make the same operations.
8x2 : x2 = 8
10x − 6 is the remainder, because its degree is less than the divisor it is not possible to continue dividing.
x3 +2x2 + 5x + 8 is the quotient.