Chapter 12: Mock Test
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Questions and Answers
- 1.
2x^2 – 16 is a difference of two squares.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
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.)Rate this question:
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- 2.
X^2 – 4 is a square of the difference.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
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 TrinomialsRate this question:
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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
Correct Answer
B. FalseExplanation
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.Rate this question:
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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
Correct Answer
B. FalseExplanation
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]Rate this question:
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- 5.
4 is the missing term in x^2 -___x + 3
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
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.Rate this question:
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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
Correct Answer
B. FalseExplanation
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.Rate this question:
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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
Correct Answer
D. 12x and 6Explanation
This is a perfect square trinomial.Rate this question:
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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)
Correct Answer
B. (a - d)Explanation
This is again factoring by grouping.Rate this question:
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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
Correct Answer
C. 9 and 3Explanation
This is a difference of two squares pattern.Rate this question:
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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
Correct Answer
D. 5, 7 and 6x^2Explanation
This is factoring complex trinomials.Rate this question:
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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
Correct Answer
A. -5Explanation
This is factoring by groupingRate this question:
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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
Correct Answer
7
x = 7
X=7
X = 7
x=7Explanation
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
Answer:
the only sensible andwer to this question is 7. because there is no such thing as a -10 number of eggs.Rate this question:
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Mar 21, 2023Quiz Edited by
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