Chapter 12: Mock Test

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

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.

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

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

Submit

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

True

False

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]

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]

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

-5

5

-5k

Greatest Common Factor

This is factoring by grouping

Explanation

This is factoring by grouping

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

(a +d)

(a - d)

(d + a)

(d – a)

This is again factoring by grouping.

Explanation

This is again factoring by grouping.

5. if x^2 – 1 = (x + 1)(x – 1); then x^2 + 1 = (x + 1)(x + 1)

True

False

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.

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.

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

6x and 6

9x and 6

6x and 9

12x and 6

This is a perfect square trinomial.

Explanation

This is a perfect square trinomial.

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

6 and 2

2 and 6

9 and 3

3 and 9

This is a difference of two squares pattern.

Explanation

This is a difference of two squares pattern.

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

True

False

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.

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.

9. 2x^2 – 16 is a difference of two squares.

True

False

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.)

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.)

10. 4 is the missing term in x^2 -___x + 3

True

False

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.

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.

11. x^2 – 4 is a square of the difference.

True

False

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

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

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

5, 7 and 5x^2

7, 5 and 5x^2

7, 5 and 6x^2

5, 7 and 6x^2

This is factoring complex trinomials.

Explanation

This is factoring complex trinomials.