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Worksheets

Chapter 5

Total questions: 10

Worksheet time: 27mins

Name
Class
Date
1.

Simplify:

 (3xmy3)3n(2x4y5)2n\left(-3x^my^3\right)^{3n}\left(2x^4y^5\right)^{2n}  

a)

 (108)nx(3mn+8n)y19n\left(-108\right)^nx^{\left(3mn+8n\right)}y^{19n}  

b)

 (23)nx(3mn+8n)y19n\left(-23\right)^nx^{\left(3mn+8n\right)}y^{19n}  

c)

 (6)5nx11mny19n\left(-6\right)^{5n}x^{11mn}y^{19n}  

d)

 (1)nx11mny16n\left(-1\right)^nx^{11mn}y^{16n}  

2.

Simplify:

 (27a5b7c515a9b12c8)3\left(\frac{27a^{-5}b^7c^5}{15a^{-9}b^{12}c^{-8}}\right)^{-3}  

a)

 125b15c9729a12\frac{125b^{15}c^9}{729a^{12}}  

b)

 125b15729a12c39\frac{125b^{15}}{729a^{12}c^{39}}  

c)

 27a1215b15c9\frac{27a^{12}}{15b^{15}c^9}  

d)

 9a4c135b5\frac{9a^4c^{13}}{5b^5}  

3.

Identify the degree of and write the polynomial in standard form.

 4x3yz+9xy7z25x2y3z23xyz4x^3yz+9xy^7z^2-5x^2y^3z^2-3xyz  

a)

 9xy7z25x2y3z2+4x3yz3xyz9xy^7z^2-5x^2y^3z^2+4x^3yz-3xyz  ; degree: 25

b)

 3xyz+4x3yz5x2y3z2+9xy7z2-3xyz+4x^3yz-5x^2y^3z^2+9xy^7z^2  ; degree 25

c)

 3xyz+4x3yz5x2y3z2+9xy7z2-3xyz+4x^3yz-5x^2y^3z^2+9xy^7z^2  ; degree 9

d)

 9xy7z25x2y3z2+4x3yz3xyz9xy^7z^2-5x^2y^3z^2+4x^3yz-3xyz  ; degree: 10

4.

Simplify:

 (5x8z)2\left(5x-8z\right)^2  

a)

 25x264z225x^2-64z^2  

b)

 25x2+64z225x^2+64z^2  

c)

 25x280xz+64z225x^2-80xz+64z^2  

d)

 (5x8z)2\left(5x-8z\right)^2  

5.

Factor completely:

 16x4625y416x^4-625y^4  

a)

 (2x5y)(2x+5y)(4x2+25y2)\left(2x-5y\right)\left(2x+5y\right)\left(4x^2+25y^2\right)  

b)

 (2x5y)(2x+5y)(2x5y)(2x+5y)\left(2x-5y\right)\left(2x+5y\right)\left(2x-5y\right)\left(2x+5y\right)  

c)

 (4x225y2)(4x2+25y2)\left(4x^2-25y^2\right)\left(4x^2+25y^2\right)  

d)

 (4x25y)(4x+25y)\left(4x-25y\right)\left(4x+25y\right)  

6.

Factor completely:

 2x495x21472x^4-95x^2-147  

a)

 (x249)(x2+3)\left(x^2-49\right)\left(x^2+3\right)  

b)

 (x49)(x+3)\left(x-49\right)\left(x+3\right)  

c)

Not Factorable

d)

 (x7)(x+7)(2x2+3)\left(x-7\right)\left(x+7\right)\left(2x^2+3\right)  

7.

Solve for x:

 15x234x+16=015x^2-34x+16=0  

a)

 x={2, 8}x=\left\{2,\ 8\right\}  

b)

 x={23, 85}x=\left\{\frac{2}{3},\ \frac{8}{5}\right\}  

c)

 x={3, 5}x=\left\{3,\ 5\right\}  

d)

 x={85, 23}x=\left\{-\frac{8}{5},\ -\frac{2}{3}\right\}  

8.

Solve for x:

 48x3110x2+95x=5x(2x+4)48x^3-110x^2+95x=5x\left(2x+4\right)  

a)

 x={0, 54}x=\left\{0,\ \frac{5}{4}\right\}  

b)

 x={54}x=\left\{\frac{5}{4}\right\}  

c)

 x={54, 54}x=\left\{-\frac{5}{4},\ \frac{5}{4}\right\}  

d)

No Solution

9.

The difference of two positive numbers is 12. The sum of their squares is 314. What are the two numbers?

a)

18 and 6

b)

17 and 5

c)

13 and 1

d)

15 and 3

10.

Kevin is building a path of uniform width around his 14 ft by 9 ft garden. If the area of the path is 78 square feet, what is the width of the path?

a)

52 feet

b)

13 feet

c)

6 feet

d)

1.5 feet