Cumulative test, Lessons 8-10

Lesson 8     Common factors
Lesson 9     Difference of squares
Lesson 10   Difference and sum of cubes

This cumulative test is an summative assessment that will allow you to measure your comprehension of the mathematical notions presented in Lessons 8,9 and 10.

Before proceeding to answer the questions, ensure that you have a pencil and some paper in your possession.

You may begin the first question, or review the lessons if you wish.

For each question, click on the box corresponding to your answer, and then click on the 'Submit Answer' button.

1- Remove common factors, or decompose into factors as the problem requires.
4h3-6h2+2h

h(4h2-6h+2)
2h(2h2-3h+1)
2h(2h2-3h)
2h(2h-1)(h-1)
     


2- Remove common factors, or decompose into factors as the problem requires.
10xy+15x-6yz-9z
(2y+3)(5x-3z) 5x(2y+3)-3z(2y+3) Neither of these answers is correct.
     


3- Remove common factors, or decompose into factors as the problem requires.
3a2b5(x+y)4-9a3b2(x+y)3+12a2b3(x+y)2

3a2b2(x+y)2[b3(x+y)2
-3a(x+y)+4b]
3a2b2(x+y)2[b3(x+y)2
-3ax-3ay+4b]
Neither of these answers is correct.
     


4- Remove common factors, or decompose into factors as the problem requires.
9-b2
(b-3)(b+3) (3-b)2 (3-b)(3+b)


5- Remove common factors, or decompose into factors as the problem requires.
81p2-49q2
(9p+7q)(9p-7q) (9p-7q)(9p+7q) No common factor may be removed.
     


6- Remove common factors, or decompose into factors as the problem requires.
16x4-81
(4x2+9)(4x2-9) (4x2+9)(2x+3)(2x-3) (2x+3)3(2x-3)
     


7- Remove common factors, or decompose into factors as the problem requires.
(x+h)2 - x2
h(2x+h) (x+h+x)(x+h-x) h2
     


8- Remove common factors, or decompose into factors as the problem requires.
m3-27n3

(m+3n)(m2-3mn+9n2)
(m-3n)(m2+3mn+9n2)
(m-3n)(m2+6mn+9n2)
     


9- Decompose into factors and simplify.



(x+h)2+(x+h)x+x2

Neither of these answers is correct.
     


10- Decompose into factors and simplify.
(x+y)3-(x-y)3

0
2y[(x+y)2+(x+y)(x-y)+(x-y)2]
[(x+y)-(x-y)][(x+y)2+(x+y)(x-y)+(x-y)2]