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Example 6.86 from Elementary Algebra, 6.6 Divide Polynomials
Divide Polynomials: example 6.86
Find the quotient:
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Write it as a long division problem. Be sure the dividend is in standard form. Divide x3 by x.
Put the answer, x2, in the quotient over the x2 term.
Multiply x2 times x + 1. Line up the like terms under the dividend.Subtract x3 + x2 from x3 − x2 by changing the signs and adding.
Then bring down the next term.Divide −2x2 by x.
Put the answer, −2x, in the quotient over the x term.
Multiply −2x times x + 1. Line up the like terms under the dividend.Subtract −2x2 − 2x from −2x2 + x by changing the signs and adding.
Then bring down the last term.Divide 3x by x.
Put the answer, 3, in the quotient over the constant term.
Multiply 3 times x + 1. Line up the like terms under the dividend.Subtract 3x + 3 from 3x + 4 by changing the signs and adding.
Write the remainder as a fraction with the divisor as the denominator.To check, multiply
The result should be .
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Find the quotient:
How did it go?