Question 1

Factor out the greatest common factor. Simplify the factors, if possible.
-$$\mathrm { t } ( 3 - \mathrm { m } ) + \mathrm { s } ( 3 - \mathrm { m } )$$

Accepted Answer

A)  $t ( 3 - m ) + s$ 
B)  $( t + s ) ( 3 + m )$ 
C)  $( t - s ) ( 3 - m )$ 
D)  $( t + s ) ( 3 - m )$ 
A)  $t ( 3 - m ) + s$ 
B)  $( t + s ) ( 3 + m )$ 
C)  $( t - s ) ( 3 - m )$ 
D)  $( t + s ) ( 3 - m )$

Question 2

Factor the trinomial, if possible.
-$12 x ^ { 2 } - 52 x - 40$

Accepted Answer

A)  $4 ( 3 x + 2 ) ( x - 5 )$ 
B)  $( 12 x + 8 ) ( x - 5 )$ 
C)  $( 3 x + 2 ) ( 4 x - 20 )$ 
D)  $4 ( 3 x - 2 ) ( x + 5 )$ 
A)  $4 ( 3 x + 2 ) ( x - 5 )$ 
B)  $( 12 x + 8 ) ( x - 5 )$ 
C)  $( 3 x + 2 ) ( 4 x - 20 )$ 
D)  $4 ( 3 x - 2 ) ( x + 5 )$

Question 3

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 9 } - \sqrt { 196 }$

Accepted Answer

A)  $- \sqrt { 187 }$ 
B)  $- 5.5$ 
C)  $- \sqrt { 11 }$ 
D)  $- 11$ 
A)  $- \sqrt { 187 }$ 
B)  $- 5.5$ 
C)  $- \sqrt { 11 }$ 
D)  $- 11$

Question 4

Determine the degree of the polynomial.
-$- 6 a ^ { 4 } - 14 a ^ { 2 } + 5 a + 7 a ^ { 6 }$

Accepted Answer

A)  6 
B)  13 
C)  4 
D)  12 
A)  6 
B)  13 
C)  4 
D)  12

Question 5

Factor by any method.
-$15 x ^ { 6 } - 25 x ^ { 3 } y ^ { 2 } + 12 x ^ { 3 } y ^ { 2 } - 20 y ^ { 4 }$

Accepted Answer

A)  $\left( 15 x ^ { 3 } + 4 y ^ { 2 } \right) \left( x ^ { 3 } - 5 y ^ { 2 } \right)$ 
B)  $\left( 5 x ^ { 3 } + 4 y ^ { 2 } \right) \left( 3 x ^ { 3 } - 5 y ^ { 2 } \right)$ 
C)  $\left( 5 x ^ { 3 } - 4 y ^ { 2 } \right) \left( 3 x ^ { 3 } + 5 y ^ { 2 } \right)$ 
D)  $\left( 5 x ^ { 3 } + 4 y \right) \left( 3 x ^ { 3 } - 5 y ^ { 4 } \right)$ 
A)  $\left( 15 x ^ { 3 } + 4 y ^ { 2 } \right) \left( x ^ { 3 } - 5 y ^ { 2 } \right)$ 
B)  $\left( 5 x ^ { 3 } + 4 y ^ { 2 } \right) \left( 3 x ^ { 3 } - 5 y ^ { 2 } \right)$ 
C)  $\left( 5 x ^ { 3 } - 4 y ^ { 2 } \right) \left( 3 x ^ { 3 } + 5 y ^ { 2 } \right)$ 
D)  $\left( 5 x ^ { 3 } + 4 y \right) \left( 3 x ^ { 3 } - 5 y ^ { 4 } \right)$

Question 6

Find the product.
-$$\left( 4 m ^ { 2 } \right) \left( 3 m ^ { 2 } \right)$$

Accepted Answer

A)  $- 12 \mathrm {~m}$ 
B)  $12 m ^ { 4 }$ 
C)  $- 12 m ^ { 4 }$ 
D)  $12 \mathrm {~m}$ 
A)  $- 12 \mathrm {~m}$ 
B)  $12 m ^ { 4 }$ 
C)  $- 12 m ^ { 4 }$ 
D)  $12 \mathrm {~m}$

Question 7

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$$\frac { | - 1 | } { | 5 | } = \left| \frac { - 1 } { 5 } \right|$$

Accepted Answer

A)  True 
B)  False; $\frac { | - 1 | } { | 5 | } = \left| \frac { 1 } { - 5 } \right|$ 
A)  True 
B)  False; $\frac { | - 1 | } { | 5 | } = \left| \frac { 1 } { - 5 } \right|$

Question 8

Evaluate the expression.
-Let $x = 16 , y = 21$. Evaluate $| y - x |$.

Accepted Answer

A)  5 
B)  37 
C)  $- 5$ 
D)  $- 37$ 
A)  5 
B)  37 
C)  $- 5$ 
D)  $- 37$

Question 9

Find the product.
-$$( 2 x + 9 y ) ^ { 2 }$$

Accepted Answer

A)  $4 x ^ { 2 } + 36 x y + 81 y ^ { 2 }$ 
B)  $4 x ^ { 2 } + 81 y ^ { 2 }$ 
C)  $2 x ^ { 2 } + 81 y ^ { 2 }$ 
D)  $2 x ^ { 2 } + 36 x y + 81 y ^ { 2 }$ 
A)  $4 x ^ { 2 } + 36 x y + 81 y ^ { 2 }$ 
B)  $4 x ^ { 2 } + 81 y ^ { 2 }$ 
C)  $2 x ^ { 2 } + 81 y ^ { 2 }$ 
D)  $2 x ^ { 2 } + 36 x y + 81 y ^ { 2 }$

Question 10

Evaluate the expression.
-$3 ^ { 3 }$

Accepted Answer

A)  $2.7$ 
B)  81 
C)  9 
D)  27 
A)  $2.7$ 
B)  81 
C)  9 
D)  27

Question 11

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { \frac { 18 } { x } }$

Accepted Answer

A)  $\frac { \sqrt { 3 x } } { x }$ 
B)  $3 \sqrt { 2 x }$ 
C)  $3 \sqrt { \frac { 2 } { x } }$ 
D)  $\frac { 3 \sqrt { 2 x } } { x }$ 
A)  $\frac { \sqrt { 3 x } } { x }$ 
B)  $3 \sqrt { 2 x }$ 
C)  $3 \sqrt { \frac { 2 } { x } }$ 
D)  $\frac { 3 \sqrt { 2 x } } { x }$

Question 12

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { \frac { 20 x ^ { 2 } y } { 49 } }$$

Accepted Answer

A)  $\frac { 2 \sqrt { 5 x ^ { 2 } y } } { 7 }$ 
B)  $4 x \sqrt { 5 y }$ 
C)  $x \sqrt { \frac { 20 y } { 7 } }$ 
D)  $\frac { 2 x \sqrt { 5 y } } { 7 }$ 
A)  $\frac { 2 \sqrt { 5 x ^ { 2 } y } } { 7 }$ 
B)  $4 x \sqrt { 5 y }$ 
C)  $x \sqrt { \frac { 20 y } { 7 } }$ 
D)  $\frac { 2 x \sqrt { 5 y } } { 7 }$

Question 13

Evaluate the expression.
-$$- \left| - \frac { 8 } { 9 } \right|$$

Accepted Answer

A)  $\frac { 8 } { 9 }$ 
B)  $- \frac { 8 } { 9 }$ 
C)  $\pm \frac { 8 } { 9 }$ 
D)  0 
A)  $\frac { 8 } { 9 }$ 
B)  $- \frac { 8 } { 9 }$ 
C)  $\pm \frac { 8 } { 9 }$ 
D)  0

Question 14

Factor by grouping.
-$15 x ^ { 8 } + 6 x ^ { 4 } y ^ { 4 } + 20 x ^ { 4 } y ^ { 4 } + 8 y ^ { 8 }$

Accepted Answer

A)  $\left( 3 x ^ { 4 } + 4 y \right) \left( 5 x ^ { 4 } + 2 y ^ { 8 } \right)$ 
B)  $\left( 3 x ^ { 4 } + 4 y ^ { 4 } \right) \left( 5 x ^ { 4 } + 2 y ^ { 4 } \right)$ 
C)  $\left( 15 x ^ { 4 } + 4 y ^ { 4 } \right) \left( x ^ { 4 } + 2 y ^ { 4 } \right)$ 
D)  $\left( 3 x ^ { 4 } - 4 y ^ { 4 } \right) \left( 5 x ^ { 4 } - 2 y ^ { 4 } \right)$ 
A)  $\left( 3 x ^ { 4 } + 4 y \right) \left( 5 x ^ { 4 } + 2 y ^ { 8 } \right)$ 
B)  $\left( 3 x ^ { 4 } + 4 y ^ { 4 } \right) \left( 5 x ^ { 4 } + 2 y ^ { 4 } \right)$ 
C)  $\left( 15 x ^ { 4 } + 4 y ^ { 4 } \right) \left( x ^ { 4 } + 2 y ^ { 4 } \right)$ 
D)  $\left( 3 x ^ { 4 } - 4 y ^ { 4 } \right) \left( 5 x ^ { 4 } - 2 y ^ { 4 } \right)$

Question 15

Find the product.
-$$( 5 x - 2 ) ^ { 4 }$$

Accepted Answer

A)  $- 1250 x ^ { 4 } + 2000 x ^ { 3 } + 600 x ^ { 2 } + 320 x + 16$ 
B)  $625 x ^ { 3 } - 1000 x ^ { 2 } + 600 x - 160$ 
C)  $625 x ^ { 4 } - 1000 x ^ { 3 } + 600 x ^ { 2 } - 160 x + 16$ 
D)  $\left( 25 x ^ { 2 } - 10 x + 4 \right) ^ { 4 }$ 
A)  $- 1250 x ^ { 4 } + 2000 x ^ { 3 } + 600 x ^ { 2 } + 320 x + 16$ 
B)  $625 x ^ { 3 } - 1000 x ^ { 2 } + 600 x - 160$ 
C)  $625 x ^ { 4 } - 1000 x ^ { 3 } + 600 x ^ { 2 } - 160 x + 16$ 
D)  $\left( 25 x ^ { 2 } - 10 x + 4 \right) ^ { 4 }$

Question 16

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 2 } - \frac { 1 } { x ^ { 2 } + 2 } \right)$$

Accepted Answer

A)  $\frac { 2 x } { \left( ( x + h ) ^ { 2 } + 2 \right) }$ 
B)  $\frac { - 2 x - h } { \left( ( x + h ) ^ { 2 } + 2 \right) \left( x ^ { 2 } + 2 \right) }$ 
C)  $\frac { 2 x + h } { \left( ( x + h ) ^ { 2 } + 2 \right) \left( x ^ { 2 } + 2 \right) }$ 
D)  $\frac { - 2 x + h } { ( x + h ) ^ { 2 } \left( x ^ { 2 } + 2 \right) }$ 
A)  $\frac { 2 x } { \left( ( x + h ) ^ { 2 } + 2 \right) }$ 
B)  $\frac { - 2 x - h } { \left( ( x + h ) ^ { 2 } + 2 \right) \left( x ^ { 2 } + 2 \right) }$ 
C)  $\frac { 2 x + h } { \left( ( x + h ) ^ { 2 } + 2 \right) \left( x ^ { 2 } + 2 \right) }$ 
D)  $\frac { - 2 x + h } { ( x + h ) ^ { 2 } \left( x ^ { 2 } + 2 \right) }$

Question 17

Factor the trinomial, if possible.
-$12 x ^ { 2 } + 7 x y - 12 y ^ { 2 }$

Accepted Answer

A)  $( 4 x - 3 y ) ( 3 x + 4 y )$ 
B)  $( 12 x - 3 y ) ( x + 4 y )$ 
C)  $( 4 x + 3 y ) ( 3 x - 4 y )$ 
D)  prime 
A)  $( 4 x - 3 y ) ( 3 x + 4 y )$ 
B)  $( 12 x - 3 y ) ( x + 4 y )$ 
C)  $( 4 x + 3 y ) ( 3 x - 4 y )$ 
D)  prime

Question 18

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { x _ { y } ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 13 } y ^ { 11 } }$$

Accepted Answer

A)  $x ^ { 4 } y ^ { 5 } \sqrt [ 3 ] { x ^ { 2 } y }$ 
B)  $x ^ { 4 } y 5 \sqrt [ 3 ] { x y ^ { 2 } }$ 
C)  $x ^ { 4 } y ^ { 6 } \sqrt [ 3 ] { x y }$ 
D)  $x ^ { 4 } y 5 \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } }$ 
A)  $x ^ { 4 } y ^ { 5 } \sqrt [ 3 ] { x ^ { 2 } y }$ 
B)  $x ^ { 4 } y 5 \sqrt [ 3 ] { x y ^ { 2 } }$ 
C)  $x ^ { 4 } y ^ { 6 } \sqrt [ 3 ] { x y }$ 
D)  $x ^ { 4 } y 5 \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } }$

Question 19

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { \left( 3 x ^ { 3 } y ^ { 5 } \right) ^ { 6 } } { 9 x y ^ { 2 } }$

Accepted Answer

A)  $81 x ^ { 8 } y ^ { 9 }$ 
B)  $81 x ^ { 17 } y ^ { 28 }$ 
C)  $\frac { x ^ { 17 } y ^ { 28 } } { 3 }$ 
D)  $\frac { x ^ { 8 } y ^ { 9 } } { 3 }$ 
A)  $81 x ^ { 8 } y ^ { 9 }$ 
B)  $81 x ^ { 17 } y ^ { 28 }$ 
C)  $\frac { x ^ { 17 } y ^ { 28 } } { 3 }$ 
D)  $\frac { x ^ { 8 } y ^ { 9 } } { 3 }$

Question 20

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$( - 4 x ) ^ { 0 }$

Accepted Answer

A)  1 
B)  0 
C)  4 
D)  -1 
A)  1 
B)  0 
C)  4 
D)  -1

Factor out the greatest common factor. Simplify the factors, if possible. - $\mathrm { t } ( 3 - \mathrm { m } ) + \mathrm { s } ( 3 - \mathrm { m } )$

Factor the trinomial, if possible. - $12 x ^ { 2 } - 52 x - 40$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 9 } - \sqrt { 196 }$

Determine the degree of the polynomial. - $- 6 a ^ { 4 } - 14 a ^ { 2 } + 5 a + 7 a ^ { 6 }$

Factor by any method. - $15 x ^ { 6 } - 25 x ^ { 3 } y ^ { 2 } + 12 x ^ { 3 } y ^ { 2 } - 20 y ^ { 4 }$

Find the product. - $\left( 4 m ^ { 2 } \right) \left( 3 m ^ { 2 } \right)$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $\frac { | - 1 | } { | 5 | } = \left| \frac { - 1 } { 5 } \right|$

Evaluate the expression. -Let $x = 16 , y = 21$ . Evaluate $| y - x |$ .

Find the product. - $( 2 x + 9 y ) ^ { 2 }$

Evaluate the expression. - $3 ^ { 3 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 18 } { x } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 20 x ^ { 2 } y } { 49 } }$

Evaluate the expression. - $- \left| - \frac { 8 } { 9 } \right|$

Factor by grouping. - $15 x ^ { 8 } + 6 x ^ { 4 } y ^ { 4 } + 20 x ^ { 4 } y ^ { 4 } + 8 y ^ { 8 }$

Find the product. - $( 5 x - 2 ) ^ { 4 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 2 } - \frac { 1 } { x ^ { 2 } + 2 } \right)$

Factor the trinomial, if possible. - $12 x ^ { 2 } + 7 x y - 12 y ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { x _ { y } ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 13 } y ^ { 11 } }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { \left( 3 x ^ { 3 } y ^ { 5 } \right) ^ { 6 } } { 9 x y ^ { 2 } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( - 4 x ) ^ { 0 }$

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Exam 12: Review of Basic Concepts

Factor out the greatest common factor. Simplify the factors, if possible. - t(3−m)+s(3−m)\mathrm { t } ( 3 - \mathrm { m } ) + \mathrm { s } ( 3 - \mathrm { m } )t(3−m)+s(3−m)

Factor the trinomial, if possible. - 12x2−52x−4012 x ^ { 2 } - 52 x - 4012x2−52x−40

Simplify the expression. Assume all variables represent positive real numbers. - 9−196\sqrt { 9 } - \sqrt { 196 }9​−196​

Determine the degree of the polynomial. - −6a4−14a2+5a+7a6- 6 a ^ { 4 } - 14 a ^ { 2 } + 5 a + 7 a ^ { 6 }−6a4−14a2+5a+7a6

Factor by any method. - 15x6−25x3y2+12x3y2−20y415 x ^ { 6 } - 25 x ^ { 3 } y ^ { 2 } + 12 x ^ { 3 } y ^ { 2 } - 20 y ^ { 4 }15x6−25x3y2+12x3y2−20y4

Find the product. - (4m2)(3m2)\left( 4 m ^ { 2 } \right) \left( 3 m ^ { 2 } \right)(4m2)(3m2)

Decide whether the statement is true or false. If false, correct the statement so it is true. - ∣−1∣∣5∣=∣−15∣\frac { | - 1 | } { | 5 | } = \left| \frac { - 1 } { 5 } \right|∣5∣∣−1∣​=​5−1​​

Evaluate the expression. -Let x=16,y=21x = 16 , y = 21x=16,y=21 . Evaluate ∣y−x∣| y - x |∣y−x∣ .

Find the product. - (2x+9y)2( 2 x + 9 y ) ^ { 2 }(2x+9y)2

Evaluate the expression. - 333 ^ { 3 }33

Simplify the expression. Assume all variables represent positive real numbers. - 18x\sqrt { \frac { 18 } { x } }x18​​

Simplify the expression. Assume all variables represent positive real numbers. - 20x2y49\sqrt { \frac { 20 x ^ { 2 } y } { 49 } }4920x2y​​

Evaluate the expression. - −∣−89∣- \left| - \frac { 8 } { 9 } \right|−​−98​​

Factor by grouping. - 15x8+6x4y4+20x4y4+8y815 x ^ { 8 } + 6 x ^ { 4 } y ^ { 4 } + 20 x ^ { 4 } y ^ { 4 } + 8 y ^ { 8 }15x8+6x4y4+20x4y4+8y8

Find the product. - (5x−2)4( 5 x - 2 ) ^ { 4 }(5x−2)4

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 1h(1(x+h)2+2−1x2+2)\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 2 } - \frac { 1 } { x ^ { 2 } + 2 } \right)h1​((x+h)2+21​−x2+21​)

Factor the trinomial, if possible. - 12x2+7xy−12y212 x ^ { 2 } + 7 x y - 12 y ^ { 2 }12x2+7xy−12y2

Simplify the expression. Assume all variables represent positive real numbers. - xy53⋅x13y113\sqrt [ 3 ] { x _ { y } ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 13 } y ^ { 11 } }3xy5​​⋅3x13y11​

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - (3x3y5)69xy2\frac { \left( 3 x ^ { 3 } y ^ { 5 } \right) ^ { 6 } } { 9 x y ^ { 2 } }9xy2(3x3y5)6​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (−4x)0( - 4 x ) ^ { 0 }(−4x)0