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Polynomials

Division

We say D is a factor of P if P = D×Q for some Q.

In this case .

Determining Q from is usually carried out by long division, a method similar to that for numbers.

Example

Write each polynomial with terms in descending powers of x.

The highest term in the numerator is x³. The highest term in the denominator is x.

Start by dividing the highest term in the numerator by the highest term in the denominator, that is, dividing x into x³.

More Examples (this will open in a new window)

Exercise

Compute the polynomial division below. Check your answer when complete.

If D is not a factor of P, then     P = D×Q + R,      where R is a polynomial of degree smaller than that of D.

Hence, .

Example

More Exercises (this will open in a new window)

Exercise

Compute the polynomial division below. Write your answer with powers in increasing order and don't type blank spaces in your answer.

<< Multiplying Polynomials | Polynomials Index | Remainder Theorem >>