# Chapter 12: Mock Test

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Quizzes Created: 2 | Total Attempts: 44,670
Questions: 12 | Attempts: 111

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• 1.

### 2x^2 – 16 is a difference of two squares.

• A.

True

• B.

False

B. False
Explanation
To answer this check each term if it is a perfect square.
Is – 16 a perfect square? (yes!)
Is 2x^2 a perfect square? (NO, because the coefficient is 2. and 2 is not a perfect square.)

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• 2.

### X^2 – 4 is a square of the difference.

• A.

True

• B.

False

B. False
Explanation
Pay careful attention on the terminologies presented in chapter 12, for it can not be interchanged. Because changing it would change its meaning. This is true to the following terms:
Zero Product Property
Difference of two Squares
Sum and Difference of two Cubes
and
Perfect square Trinomials

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• 3.

### If x^2 – 1 = (x + 1)(x – 1); then x^2 + 1 = (x + 1)(x + 1)

• A.

True

• B.

False

B. False
Explanation
x^2 – 1 is a difference of two squares, that’s why it can be factored. But x^2 + 1 is a sum… we can not factor a sum of two squares.

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• 4.

### Polynomials can either be a sum or difference of terms; factoring will not affect this operation.

• A.

True

• B.

False

B. False
Explanation
Factoring transforms a polynomial to its products, thus changing the operation to multiplication.
Ex: x^2 + 2x + 1 [a sum] = (x+1)(x+1) [the parenthesis means multiply]

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• 5.

### 4 is the missing term in x^2 -___x + 3

• A.

True

• B.

False

A. True
Explanation
Check out the sign of the last term.
It’s positive, right?
if it is, it means add the factors of three or find the sum of OI in FOIL. On the other hand, if it’s ‘–‘ it means subtract or find the difference of OI in FOIL.

Thus, the missing terms is the sum of the factors of 3... or just simply the sum of 3 and 1, which is 4.

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• 6.

### If 2 is common in ‘2xy + 2xz’, then the GCF of the binomial is 2 and its factors are 2 and xy + xz.

• A.

True

• B.

False

B. False
Explanation
The Greatest Common Factor (GCF) is the biggest value, or number of common factors, a polynomial can have. In this light, notice that 2x is common on both terms.
‘2xy + 2xz’
This means that 2x is the GCF. And that the factored forms is 2x and y + z.

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• 7.

### Complete the missing terms: X^2 + ___ + 36 = (x + ___)(x+ 6)

• A.

6x and 6

• B.

9x and 6

• C.

6x and 9

• D.

12x and 6

D. 12x and 6
Explanation
This is a perfect square trinomial.

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• 8.

### Find the missing term: a(c + d) – b(c + d) = ______ (c + d)

• A.

(a +d)

• B.

(a - d)

• C.

(d + a)

• D.

(d – a)

B. (a - d)
Explanation
This is again factoring by grouping.

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• 9.

### Complete the equation: 4x^2 – ___ = (2x + 3)(2x - ___)

• A.

6 and 2

• B.

2 and 6

• C.

9 and 3

• D.

3 and 9

C. 9 and 3
Explanation
This is a difference of two squares pattern.

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• 10.

### Find the missing terms: (2x - ___)(3x + ___) = ___ - x – 35

• A.

5, 7 and 5x^2

• B.

7, 5 and 5x^2

• C.

7, 5 and 6x^2

• D.

5, 7 and 6x^2

D. 5, 7 and 6x^2
Explanation
This is factoring complex trinomials.

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• 11.

### Find the missing term: -5k + 10m – 15n = ___(k – 2m + 3n)

• A.

-5

• B.

5

• C.

-5k

• D.

Greatest Common Factor

A. -5
Explanation
This is factoring by grouping

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• 12.

### Problem solving If 35 = x^2 + 3x is the number of bottles you drink a day. Find all possible values for x.                 2

7
x = 7
X=7
X = 7
x=7
Explanation
Solution:

70 = x^2 + 3x multiply both sides by two
0 = x^2 + 3x – 70 subtract both sides by 70
0 = (x+10)(x-7) factor out

Using Zero Product Property, find two numbers that will make the equation true.

X= - 10
Checking:
0 = ( - 10+10)(x-7)
0 = 0(x-7)
0 = 0

X = 7
0 = (x+10)(7-7)
0 = (x + 10) 0
0 = 0

the only sensible andwer to this question is 7. because there is no such thing as a -10 number of eggs.

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• Current Version
• Jul 17, 2024
Quiz Edited by
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• Feb 16, 2010
Quiz Created by
Marvinjaybaclay

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