14 March 2011
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14 March 2011 Algebra 2
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14 March 2011. Algebra 2. Composition of Functions. (3x – 1)*(x 2 + 3x – 4). Multiplying a Binomial and Trinomial. Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials. Composition of Functions. (3x – 1)*(x 2 + 3x – 4) 3x 3. Multiplying a Binomial and Trinomial. - PowerPoint PPT Presentation
Transcript of 14 March 2011
14 March 2011
Algebra 2
Composition of FunctionsMultiplying a
Binomial and Trinomial
(3x – 1)*(x2 + 3x – 4)
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(3x – 1)*(x2 + 3x – 4)
3x3
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(3x – 1)*(x2 + 3x – 4)
3x3 + 9x2
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(3x – 1)*(x2 + 3x – 4)
3x3 + 9x2 – 12x
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(3x – 1)*(x2 + 3x – 4)
3x3 + 9x2 – 12x – x2
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(3x – 1)*(x2 + 3x – 4)
3x3 + 9x2 – 12x – x2 – 3x
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(3x – 1)*(x2 + 3x – 4)
3x3 + 9x2 – 12x – x2 – 3x + 4
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(3x – 1)*(x2 + 3x – 4)
3x3 + 9x2 – 12x – x2 – 3x + 4
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(3x – 1)*(x2 + 3x – 4)
3x3 + 9x2 – 12x – x2 – 3x + 4
Combine like terms
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(3x – 1)*(x2 + 3x – 4)
3x3 + 9x2 – 12x – x2 – 3x + 4
Combine like terms
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(3x – 1)*(x2 + 3x – 4)
3x3 + 9x2 – 12x – x2 – 3x + 4
3x3 + 8x2 – 15x + 4
Final answer
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Multiply (x - 3)(2x2 + 3x – 5)
1. 2x3 – 3x2 – 14x + 152. 3x3 – 3x2 – 14x – 153. 2x3 – 6x2 – 9x + 154. 3x3 – 6x2 – 14x – 155. 2x3 + 3x2 + 14x - 15
Composition of FunctionsMultiplying a
Binomial and Trinomial
(2x – 3)3 = ?
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(2x – 3)3 = (2x – 3)(2x – 3)(2x – 3)
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(2x – 3)3 = (2x – 3)(2x – 3)(2x – 3)
Multiply these two using FOIL or Box method
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(2x – 3)3 = (2x – 3)(2x – 3)(2x – 3)
Multiply these two using FOIL or Box method:
2x - 3 2x
-3Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(2x – 3)3 = (2x – 3)(2x – 3)(2x – 3)
Multiply these two using FOIL or Box method:
2x - 3 2x 4x2 -6x
-3 -6x +9Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(2x – 3)3 = (2x – 3)(2x – 3)(2x – 3)
Multiply these two using FOIL or Box method:
2x - 3 2x 4x2 -6x
-3 -6x +9
4x2 – 12x + 9
Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(2x – 3)3 = (2x – 3)(2x – 3)(2x – 3)
= (2x – 3)(4x2 – 12x + 9)
Substitute the trinomial we just foundMathematics.XEI.504: (24-
27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(2x – 3)3 = (2x – 3)(2x – 3)(2x – 3)
= (2x – 3)(4x2 – 12x + 9)
8x3 – 24x2 + 18x
MultiplyMathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(2x – 3)3 = (2x – 3)(2x – 3)(2x – 3)
= (2x – 3)(4x2 – 12x + 9)
8x3 – 24x2 + 18x – 12x2 + 36x – 27
MultiplyMathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(2x – 3)3 = (2x – 3)(2x – 3)(2x – 3)
= (2x – 3)(4x2 – 12x + 9)
8x3 – 24x2 + 18x – 12x2 + 36x – 27
Combine like termsMathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Composition of FunctionsMultiplying a
Binomial and Trinomial
(2x – 3)3 = (2x – 3)(2x – 3)(2x – 3)
= (2x – 3)(4x2 – 12x + 9)
8x3 – 24x2 + 18x – 12x2 + 36x – 27
8x3 – 36x2 + 54x – 27
Final answerMathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials
Multiplying Polynomials
• Complete questions 51- 60• Write the question number on your work-sheet• Show your work on your work-sheet• Write the answer letter on your work-sheet• You have 15 minutes
Factoring PolynomialsFactoring a
common term5x + 5y + 5z = ?
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring PolynomialsFactoring a
common term5x + 5y + 5z = ?
Look for something that is the same in each term
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring PolynomialsFactoring a
common term5x + 5y + 5z = ?
Look for something that is the same in each term
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring PolynomialsFactoring a
common term5x + 5y + 5z = ?
5(x + y + z)
Write that outside a set of parentheses, and write what is left inside
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring PolynomialsFactoring a
common term4x2 + 5xy + 6xz = ?
Look for something that is the same in each term
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring PolynomialsFactoring a
common term4x2 + 5xy + 6xz = ?
Look for something that is the same in each term
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring PolynomialsFactoring a
common term4x2 + 5xy + 6xz = ?
x(4x + 5y + 6z)
Write that outside a set of parentheses, and write what is left inside
Mathematics.XEI.505: (24-27) Factor simple quadratics
opq + opr + ops = ?
1. o(pq + pr + ps)2. p(oq + or + os)3. pq(o + r + s)4. op(q + r + s)
Factoring PolynomialsDifference of
SquaresIf there are only two terms given to you, you probably have a difference of squares.
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring PolynomialsDifference of
SquaresIf there are only two terms given to you, you probably have a difference of squares.
Example: x2 – 25
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring PolynomialsDifference of
SquaresExample: x2 – 25
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring PolynomialsDifference of
SquaresExample: x2 – 25
Solution: ( )( )
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring PolynomialsDifference of
SquaresExample: x2 – 25
Solution: ( )( )
Mathematics.XEI.505: (24-27) Factor simple quadratics
xx 2
Factoring PolynomialsDifference of
SquaresExample: x2 – 25
Solution: (x )(x )
Mathematics.XEI.505: (24-27) Factor simple quadratics
xx 2
Factoring PolynomialsDifference of
SquaresExample: x2 – 25
Solution: (x )(x )
Mathematics.XEI.505: (24-27) Factor simple quadratics
525
Factoring PolynomialsDifference of
SquaresExample: x2 – 25
Solution: (x 5)(x 5)
Mathematics.XEI.505: (24-27) Factor simple quadratics
525
Factoring PolynomialsDifference of
SquaresExample: x2 – 25
Make one ‘+’ and one ‘-’
Solution: (x 5)(x 5)
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring PolynomialsDifference of
SquaresExample: x2 – 25
Make one ‘+’ and one ‘-’
Solution: (x + 5)(x - 5)
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring PolynomialsDifference of
SquaresExample: x2 – 25
Solution: (x + 5)(x - 5)
Mathematics.XEI.505: (24-27) Factor simple quadratics
Factoring Polynomials
• Complete questions 61- 70• Write the question number on your work-sheet• Show your work on your work-sheet• Write the answer letter on your work-sheet• You have 10 minutes
Factoring PolynomialsFactor a
Quadratic-Identify a,b,c
x2 + 4x - 12= 0
Mathematics.XEI.503
Factor a Quadratic
-Identify a,b,c
x2 + 4x - 12= 0
a b c
Mathematics.XEI.503
Factoring Polynomials
Factoring PolynomialsFactor a
Quadratic-Identify a,b,c
x2 + 4x - 12= 0
a b c
a = 1 b = 4 c = -12
Mathematics.XEI.503
Factoring PolynomialsFactor a
Quadratic-Multiply a and c
x2 + 4x - 12= 0
a = 1 c = -12 ac = -12
Mathematics.XEI.503
Factoring PolynomialsFactor a
Quadratic-Make a chart listing the factors of ac
ac = -12 b = 4
a c a + c =
1 -12
2 -6
3 -4
4 -3
6 -2
12 -1Mathematics.XEI.503
Factoring PolynomialsFactor a
Quadratic-Add the a and c columns
ac = -12 b = 4
a c a + c =
1 -12 -11
2 -6 -4
3 -4 -1
4 -3 1
6 -2 4
12 -1 11Mathematics.XEI.503
Factoring PolynomialsFactor a
Quadratic-Add the a and c columns
ac = -12 b = 4
Since b = 4, and 6 + -2 = 4, our factors are 6,-2.
a c a + c =
1 -12 -11
2 -6 -4
3 -4 -1
4 -3 1
6 -2 4
12 -1 11Mathematics.XEI.503
Factoring PolynomialsFactor a
Quadraticx2 + 4x - 12= 0
Factors: 6,-2
Mathematics.XEI.503
Factoring PolynomialsFactor a
Quadraticx2 + 4x - 12= 0
Factors: 6,-2
Factored Form: (x + 6)(x – 2) = 0
Mathematics.XEI.503
Factoring Polynomials
• Complete questions 71- 81• Write the question number on your work-sheet• Show your work on your work-sheet• Write the answer letter on your work-sheet• You have 15 minutes
