Alg1, Unit 13, Lesson02_absent-student, page 1
Dividing polynomials by monomials
Negative exponents
Rule: When a polynomial is divided by a monomial, make separate
fractions by placing each term in the polynomial (the numerator) over
the monomial (the denominator) and then simplify:
term1 + term2 + term3
term1 term2 term3
=
+
+
monomial
mono
mono
mono
Example 1:
Example 3:
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Example 2:
Example 4:
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Alg1, Unit 13, Lesson02_absent-student, page 2
Negative exponents:
What is the meaning of x–2?
Rule: Anytime a monomial’s position is switched between
numerator and denominator in a fraction, change the sign of the
exponent.
Why is this rule true? Consider the problem x5/x2. In lesson 13-01 we
learned to subtract the exponents and replace the larger exponent with
the result of the subtraction.
Now work the same problem using our new “change the exponent’s
sign rule” and get the same answer.
–2
Example 5: Simplify 2x + 5/x
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2
Example 6: Simplify x7x
–3
Alg1, Unit 13, Lesson02_absent-student, page 3
– –2 4 5
*Example 7: Simplify (3x2y 3) x y
Example 8: 16x/12x4
See Enrichment Topic E for an extended discussion of Scientific
Notation in which many of the concepts of exponents presented in this
lesson are used.
See Calculator Appendix L for how to use scientific notation on the
graphing calculator.
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Alg1, Unit 13, Lesson02_absent-student, page 4
Assignment: Simplify each problem.
1.
3.
5.
#
"
'( "
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2.
4.
6.
$ $ % "$ &
)**+
*
Alg1, Unit 13, Lesson02_absent-student, page 5
7.
9.
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!
-% - "- 11.
"-
! "'% ! ! !
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8.
, ,% ", 10.
",
". . ".
.
Alg1, Unit 13, Lesson02_absent-student, page 6
12.
# # " #% ") #
13. Simplify 8/x3 – 2x–3
14. x8 x–3/x2
15. Simplify (2y3 x–5)–1 y4 x–1
16. Simplify (22xy–1)/(2y3x5)
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