section 3.5polynomials of the form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... ·...
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![Page 1: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/1.jpg)
Section 3.5 Polynomials Multiplying Binomialssoln.notebook
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Section 3.5 Polynomials of the Form x2 + bx + c
![Page 2: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/2.jpg)
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1. Multiply (x + 2)(x 3) using all three methods.
A)
B)
In General,
There are 3 ways to multiply polynomials:> Algebra Tiles> Rectangle Model> Distributive Property
Multiplying Polynomials
C) Distributive Property
![Page 3: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/3.jpg)
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2. Multiply the following using the rectangle model.
A) (x + 7)(x + 5)B) (x 3)(x + 8)
C) (x 7)(x +2x 6)D) (5 x)(9 x)2
![Page 4: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/4.jpg)
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3. Multiply using the distributive property.
A) (x + 3)(x 5) B) (x 6)(x 8)
C) (x 7) D) (x + 2)(x 7)2
![Page 5: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/5.jpg)
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Multiplying Polynomials With More Than One Variable (sect. 3.7)
Example: Expand and Simplify.
A) (2x 5y)(3x2 + 2y 7)
B) (3x + 4y)(x2 2x 7y)
![Page 6: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/6.jpg)
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C) 5x2(2x 1)(4x 3)
D) (4m + 1)(3m 2) + (2m 1)(3m + 4)
![Page 7: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/7.jpg)
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Example: Write a polynomial to represent the area of the shaded region. Simplify each polynomial. Find the area if x = 2.
4x 5
3x + 8 2x
x + 3
![Page 8: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/8.jpg)
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Example: Factor x2 + 5x + 4
There are two processes we can use to factor trinomials of the form x2 + bx + c.
Factoring and multiplying are inverse processes.We can use this tofactor a trinomial.
Method 1: Algebra Tiles
Arrange the tiles of x² + 5x + 4, in a rectangle.
Factoring Trinomials of the form x2 + bx + c
x2 tiles x tilesunit tiles
Note all positve xtiles should be kept together and all negative xtiles should be kept together.
The length and width of the rectangle are the factors of the polynomial.
x tiles
![Page 9: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/9.jpg)
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Method 2:
To determine the factors of a trinomial of the form x2 + bx + c,first determine two numbers whose sum is b and whose product is c.These numbers are the constant terms in two binomial factors, eachof which has x as its first term.
![Page 10: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/10.jpg)
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![Page 11: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/11.jpg)
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Example: Factor:
a. x² + 12x + 20 b. x² 2x 8
c. a² + 7a 18 d.15x+ x2+14
e. x2 + 8x 48 f. x2 x 72
![Page 12: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/12.jpg)
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Example: Factor:
A) 30 + 7m + m² B) 24 5d + d2
Example: Factor completely. Remove GCF first. (# 21 p.167 in textbook.
A) 5h² 20h + 60 B) 4t2 16t + 128
![Page 13: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/13.jpg)
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Example: Explain why x2 + 3x + 4 cannot be factored?
Example: How many integer values are there for k for which x2 +kx +24 is factorable?
![Page 14: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/14.jpg)
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Example: Find and correct the mistakes in the factoring below.
A. Given s2 − 3s − 10,
sum = −3product = −10 numbers are −2 and 5
(s−2)(s+5)
B. Given 2x2 + 6x 40
2x2 + 6x − 40 2(x2 + 3x − 40) 2(x − 8)(x + 5)
![Page 15: Section 3.5Polynomials of the Form 2 + cmsbourgeois2016.weebly.com/uploads/5/5/9/1/55918287/... · 2019-10-02 · Section 3.5 Polynomials Multiplying Binomialssoln.notebook 9 January](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f5d0b762aae11448e7ae419/html5/thumbnails/15.jpg)
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