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We will be examining polynomials
divided by monomials and by binomials.
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Steps for Dividing a Polynomial by a
Monomial:
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Divide each term of the polynomial by the monomial. |
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a) Divide numbers
(coefficients)
b) Subtract exponents |
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Keep
this in mind
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* The number of terms in the polynomial equals the number
of terms in the answer when dividing by a monomial. |
2. Remember that numbers do not cancel and
disappear! A number divided by itself
is 1. It reduces to the number
1. |
3.
Remember to write the appropriate sign in between
the terms. |
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| Example: |
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The polynomial on
the top has 3 terms and the answer has 3 terms. |
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Notice how the numbers (the coefficients)
were divided. |
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Answer:
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Notice how the exponents were subtracted.
Notice how the last term reduced to one. |
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Think about it: |
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Dividing by a
number is the same process as multiplying by the reciprocal of
that number. |
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Notice how we used
the reciprocal of 4x2 |
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Answer:
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Now the reciprocal
was distributed across the parentheses and the problem proceeds
as in the example above. |
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Steps for Dividing a Polynomial by a
Binomial:
1.
Remember that the
terms in a binomial cannot be separated from one another
when reducing.
For example, in the binomial 2x + 3, the 2x
can never be reduced unless the entire
expression 2x + 3 is
reduced. |
2. Factor completely both
the numerator and denominator before reducing. |
3.
Divide both the numerator and denominator by their
greatest common factor. |
Examples:
(see more under "Factoring"
section)
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1. |
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Notice that the x+1
was reduced as a "set". |
| 2. |
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3. |
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4. |
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Tricky strategy: Notice that the -1
was factored out of the numerator to create a binomial
compatible with the one in the denominator.
2 - x = -1(x - 2) |
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If you are solving multiple choice
questions, you can use the calculator to
"check" your work with polynomials.
You can use a Numerical Checking process:
Numerical Process
or
You can use an Equation Checking process::
Equation Process |
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