# Dividing Polynomials

#### Solve the Division of Polynomials:

P(x) = x^{5} + 2x^{3} − x − 8

Q(x) = x^{2} − 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.

x^{5} : x^{2} = x^{3}

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.

2x^{4} : x^{2} = 2 x^{2}

Proceed as before.

5x^{3} : x^{2} = 5 x

Again, make the same operations.

8x^{2} : x^{2} = 8

10x − 6 is the** remainder**, because its degree is less than the divisor it is not possible to continue dividing.

x^{3 }+2x^{2} + 5x + 8 is the quotient.