Dividing Polynomials

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.

Dividing Polynomials

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:

Dividing Polynomials

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

Polynomial Division

Proceed as before.

5x3 : x2 = 5 x

Dividing Polynomials

Again, make the same operations.

8x2 : x2 = 8

Polynomial Division

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.