223 Reference Chapter Section R3: Polynomials Rules for Exponents Product Rule Power Rule 1 Power...
16
223 Reference Chapter Section R3: Polynomials Rules for Exponents Product Rule Power Rule 1 Power Rule 2 Power Rule 3 n m n m a a a mn n m a a ) ( ) 0 ( b b a b a m m m m m m b a ab ) (
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Transcript of 223 Reference Chapter Section R3: Polynomials Rules for Exponents Product Rule Power Rule 1 Power...
223 Reference ChapterSection R3: PolynomialsRules for ExponentsProduct Rule
Power Rule 1
Power Rule 2
Power Rule 3
nmnm aaa
mnnm aa )(
)0(
bb
a
b
am
mm
mmm baab )(
223 Reference ChapterSection R3: PolynomialsSimplify the Following:
1.
2.
3.
4.
3245 yyxx
93)(r
3
43
520
pn
mkj
642 )( cab
223 Reference ChapterSection R3: Polynomials
Simplify the Following:
1.x^9y^5
2.r^27
3.a^6b^12c^24
4.
(k^6m^15)/(n^9p^12)
3245 yyxx
93)(r
3
43
520
pn
mkj
642 )( cab
223 Reference ChapterSection R3: PolynomialsPolynomial: a finite sum of terms with only positive or zero integer coefficients permitted for the variables.
The Degree of the polynomial is the highest coefficient.
Monomial: 1 termBinomial: 2 termsTrinomial: 3 terms
Example: Here is a polynomialThe degree is 9, and it is a trinomial
784 49 tt
223 Reference ChapterSection R3: Polynomials
Adding and Subtracting Polynomials is done by combining like terms.
Example: Simplify each expression1.
2.
3.
4.
)32()425( 33 yyyy
)932()25( 4343 bbbb
)736()274( 234235 aaaaaa
)82(2)642(4 245245 xxxxxx
223 Reference ChapterSection R3: Polynomials
Adding and Subtracting Polynomials is done by combining like terms.
Example: Simplify each expression1.
7y^3 + 5y – 42.
4a^5 + 6a^4 – 4a^3 + 9a^23.
3b^3 – b^4 + 9
4. 8x^5 – 16x^4 + 24x^2 – 4x^5 – 2x^4 + 16x^2 =
4x^5 – 18x^4 + 40x^2
)32()425( 33 yyyy
)932()25( 4343 bbbb
)736()274( 234235 aaaaaa
)82(2)642(4 245245 xxxxxx
223 Reference ChapterSection R3: Polynomials
Multiplying Polynomials-multiply each term of the first polynomial by each term of the second polynomial, then combine like terms.
Example: Simplify each expression1.
2.
3.
4.
)3)(42( yy
)52)(52( xx
)2)(53( 22 aaaa
23 )64( w
223 Reference ChapterSection R3: Polynomials
Multiplying Polynomials-multiply each term of the first polynomial by each term of the second polynomial, then combine like terms.
Example: Simplify each expression1.
2y^2 + 2y - 122. 4x^2 – 25 3. a^4 – 5a^3 + 11a^2 – 10a
4. 16w^6 + 48w^3 + 36
)3)(42( yy
)52)(52( xx
)2)(53( 22 aaaa
23 )64( w
223 Reference ChapterSection R3: Polynomials
Dividing Polynomials: the quotient can be found using an algorithm similar to the long division model used for whole numbers. Both polynomials must be written in descending order.
Example: What is the quotient of 2730/65?Use the process of long division.
223 Reference ChapterSection R3: Polynomials
Dividing Polynomials: the quotient can be found using an algorithm similar to the long division model used for whole numbers. Both polynomials must be written in descending order.
Example: What is the quotient of 2730/65?Use the process of long division. 42 65)2730 260 130 130 0
223 Reference ChapterSection R3: Polynomials
Dividing Polynomials
Example: Find the quotient
)32()12710( 23 xbyxxxdivide
223 Reference ChapterSection R3: Polynomials
Dividing Polynomials
Example: Find the quotient
)32()12710( 23 xbyxxxdivide
Quotient: 5x^2 + 4x (no remainder)
223 Reference ChapterSection R3: Polynomials
Dividing Polynomials
Example: Find the quotient
)4()365( 224 xxbyxxdivide
223 Reference ChapterSection R3: Polynomials
Dividing Polynomials
Example: Find the quotient
)4()365( 224 xxbyxxdivide
Quotient: 5x^2 - 26 (remainder of 104x + 3)
223 Reference ChapterSection R3: Polynomials
Dividing Polynomials
Example: Find the quotient
)5()26( 24 abyaaadivide
223 Reference ChapterSection R3: Polynomials
Dividing Polynomials
Example: Find the quotient
)5()26( 24 abyaaadivide
Quotient: 6a^3 – 30a^2 + 150 a(remainder of -748a)
