2. Dividing by a Monomial
Write the division as a fraction and use the quotient of
powers property.
When dividing polynomials, you can check your work
using multiplication.
3. Example 1 Divide monomials
Divide –8x5 by 2x2.
SOLUTION
Write the division as a fraction and use the quotient
of powers property.
–8x5
–8x5 ÷ (2x2) = Write as fraction.
2x2
– 8 x5 Rewrite using product rule for
= • 2 fractions.
2 x
–8
= • x5 – 2 Quotient of powers property
2
10. Dividing by a Binomial
To divide a polynomial by a binomial, use long
division.
11. Example 4 Divide a polynomial by a binomial
Divide x2 + 2x – 3 by x – 1.
SOLUTION
STEP 1 Divide the first term of x2 + 2x – 3 by the first
term of x – 1.
x
x – 1 x2 + 2x – 3 Think: x2 ÷ x = ?
x2 – x Multiply x – 1 by x.
3x Subtract x2 – x from x2 + 2x.
12. Example 4 Divide a polynomial by a binomial
STEP 2 Bring down –3. Then divide the first term of
3x – 3 by the first term of x – 1.
x + 3
x – 1 x2 + 2x – 3
x2 – x
3x – 3 Think: 3x ÷ x = ?
3x – 3 Multiply x – 1 by 3.
0 Subtract 3x – 3 from 3x – 3;
remainder is 0.
ANSWER ( x2 + 2x – 3) ÷ (x – 1) = x + 3
13. Nonzero Remainders
When you obtain a nonzero remainder, apply the
following rule:
Re mainder
Dividend Divisor Quotient
Divisor
2 2
5 3 1 Which is really 1
3 3
2 12
(2 x 11x 9) (2 x 3) x 7
2x 3
14. Example 5 Divide a polynomial by a binomial
Divide 2x2 + 11x – 9 by 2x – 3.
x + 7
2x – 3 2x2 + 11x – 9
2x2 – 3x Multiply 2x – 3 by x.
14x – 9 Subtract 2x2 – 3x. Bring down – 9.
14x – 21 Multiply 2x – 3 by 7.
12 Subtract 14x – 21; remainder is 12.
12
ANSWER (2x2 + 11x – 9) ÷ ( 2x – 3) = x + 7 +
2x – 3
15. Example 6 Rewrite polynomials
Divide 5y + y2 + 4 by 2 + y.
y + 3
y + 2 y2 + 5y + 4 Rewrite polynomials.
y2 + 2y Multiply y + 2 by y.
3y + 4 Subtract y2 + 2y. Bring down 4.
3y + 6 Multiply y + 2 by 3.
–2 Subtract 3y + 6; remainder is – 2.
–2
ANSWER (5y + y2 + 4) ÷ ( 2 + y) = y + 3 +
y +2