# Division of Polynomials

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Polynomial Division
12:09 — by Khan Academy

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1 of 2 videos by Khan Academy

## Key Questions

• It is the same but just instead of getting 0 you get a polynomial in the last step.

Divide  3x^3 â€“ 5x^2 + 10x â€“ 3  by $3 x + 1$

in this case you get a polynomial seven which can be writtten in algebraic terms as $7 {x}^{0}$
so this can be proved using the division algoritm

dividend = divisor $\cdot$ quotient + remainder

• The dividend and divisor are sorted in descending order related to x.
Divide the first term of the dividend by the first divider of x.

This is the first term of the quotient.
Multiplied this term by each of the terms of the divisor and as these products have to subtract from dividing.

These products with their signs changed the writing under the similar terms with them and make the dividend reduction.

The second term of the quotient. This must be multiplied by each of the terms of the divisor and subtract the product of the dividend.

We write these terms below their similar and by the reduction gives zero residue.

I do hope you can find it useful.

• We divide each of the terms of the polynomial by the monomials separating the partial quotients with their own signs. This is the distributive law of division.

Example:

$3 {a}^{3} - 6 {a}^{2} b + 9 a {b}^{2} \div 3 a$

$\left(3 {a}^{3} - 6 {a}^{2} b + 9 a {b}^{2}\right) \div 3 a$ = $\frac{3 {a}^{3} - 6 {a}^{2} b + 9 a {b}^{2}}{3 a}$ =

$\frac{3 {a}^{3}}{3 a}$-$\frac{6 {a}^{2} b}{3 a}$+$\frac{9 a {b}^{2}}{3 a}$ = ${a}^{2} - 2 a b + 3 {b}^{2}$

I do hope you can find it useful.

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• 10:22