multiplying and dividing polynomials mfcr lesson 4-2 and 4-3 tues 1-13-15
TRANSCRIPT
Multiplying and Dividing Polynomials
MFCR Lesson 4-2 and 4-3Tues 1-13-15
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.
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) )
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
Monomial x TrinomialSimplify
Use the box method
x -y
2x
π ππβπ ππ
2 π₯ (π₯β π¦+5 )=ΒΏπ ππβπ ππ +πππ
πππ
Monomial x TrinomialSimplify
Use the box method
-2x
βπππππ ππ ππ
βππππ+π ππππβπ π ππ
βπ πππ
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
Binomial x BinomialSimplify
Group all like terms and combine for the final answer.
3x -5
5x
2
ππππ βπππ
6 -10
Binomial x BinomialSimplify
Group all like terms and combine for the final answer.
2x -1
2x
1
π ππ βπ π
2 -1
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.
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
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
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.
Dividing PolynomialsProblem Break up Simplify
Problem Break up Simplify
π ππ+π πβπ
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