multiplying and dividing polynomials mfcr lesson 4-2 and 4-3 tues 1-13-15
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Multiplying and Dividing Polynomials
MFCR Lesson 4-2 and 4-3Tues 1-13-15
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RecallRecall a monomial is a term with just term, a number, or the product of numbers and variables.
A BINOMIAL is the sum or difference of two monomials.
A TRINOMIAL is the sum or difference of three monomials.
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Multiplying Polynomials
MULTIPLYING POLYNOMIAL can be represented several different ways.
Monomials x Binomial Monomial x Trinomial
Binomial x Binomial Binomial x Trinomial
π(π+π) x
(π+π)(πβπ) )
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Multiplying Polynomials
When multiplying polynomials use the distributive property to completely simplify each expression.
MONOMIALS X BINOMIALS
Use the box method
x 4
2
π ππ 2 (π₯+4 )=ΒΏπ π+π
Use the box method
x -1
3
3 βπ 3 (π₯β1 )=ΒΏ 3
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Monomial x TrinomialSimplify
Use the box method
x -y
2x
π ππβπ ππ
2 π₯ (π₯β π¦+5 )=ΒΏπ ππβπ ππ +πππ
πππ
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Monomial x TrinomialSimplify
Use the box method
-2x
βπππππ ππ ππ
βππππ+π ππππβπ π ππ
βπ πππ
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Binomial x BinomialSimplify
Group all like terms and combine for the final answer.
Use the box method
x 3
x
7
ππ 3 π7 21
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Binomial x BinomialSimplify
Group all like terms and combine for the final answer.
3x -5
5x
2
ππππ βπππ
6 -10
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Binomial x BinomialSimplify
Group all like terms and combine for the final answer.
2x -1
2x
1
π ππ βπ π
2 -1
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Special BinomialsSimplify This binomial is being squared. When anything is raised to a power,
= =
x -3
x
-3
ππ βπ π
-3 9
multiply the binomial by itself based on the outside exponent.
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Binomial x TrinomialSimplify
-3x
π ππβπ ππ π π
ΒΏ2 π₯3β6π₯2+1 π₯2+8π₯β3 π₯+4
1 βπ π π
ΒΏπ ππβπ ππ+ππ+π
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Binomial x TrinomialSimplify
-5x
π ππβππππ π π
ΒΏ2 π₯3β10 π₯2β5π₯2+8 π₯+25 π₯β20
-5 25 βππ
ΒΏπ ππβππππ+πππβππ
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Dividing PolynomialsWhen dividing polynomials, rewrite the expression by breaking it up based on the number of terms in the numerator.
After breaking up the expression, simplify each term.
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Dividing PolynomialsProblem Break up Simplify
Problem Break up Simplify
π ππ+π πβπ
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Dividing PolynomialsSometime division can be expressed like . Rewrite the problem as a fraction and solve like normal.
Problem Rewrite Break up Simplify
2 2x 2x 32
2 2x 2x 32
2π₯2+32π₯2
2π₯2
π₯2+ 32π₯2
2