Loading…
Example 6.87 from Elementary Algebra, 6.6 Divide Polynomials
Divide Polynomials: example 6.87
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
Notice that there is no term in the dividend. We will add as a placeholder.
Write it as a long division problem. Be sure the dividend is in standard form with placeholders for missing terms. Divide x4 by x.
Put the answer, x3, in the quotient over the x3 term.
Multiply x3 times x + 2. Line up the like terms.
Subtract and then bring down the next term.Divide −2x3 by x.
Put the answer, −2x2, in the quotient over the x2 term.
Multiply −2x2 times x + 1. Line up the like terms.
Subtract and bring down the next term.Divide 3x2 by x.
Put the answer, 3x, in the quotient over the x term.
Multiply 3x times x + 1. Line up the like terms.
Subtract and bring down the next term.Divide −x by x.
Put the answer, −1, in the quotient over the constant term.
Multiply −1 times x + 1. Line up the like terms.
Change the signs, add.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?