Question 1

Find the product. $$\left( 4 s ^ { 6 } z ^ { 6 } \right) \left( 3 s ^ { 4 } z ^ { 3 } \right)$$

Accepted Answer

A)  $14 s ^ { 11 } z ^ { 10 }$ 
B)  $12 s ^ { 10 } z ^ { 9 }$ 
C)  $12 s ^ { 2 } z ^ { 3 }$ 
D)  $12 s ^ { 24 } z ^ { 18 }$ 
E)  $7 s ^ { 10 } z ^ { 9 }$ 
A)  $14 s ^ { 11 } z ^ { 10 }$ 
B)  $12 s ^ { 10 } z ^ { 9 }$ 
C)  $12 s ^ { 2 } z ^ { 3 }$ 
D)  $12 s ^ { 24 } z ^ { 18 }$ 
E)  $7 s ^ { 10 } z ^ { 9 }$

Question 2

Raise the monomial to the indicated power. $\left( a b ^ { 6 } c ^ { 3 } \right) ^ { 2 }$

Accepted Answer

A)  $a ^ { 2 } b ^ { 8 } c ^ { 5 }$ 
B)  $a ^ { 3 } b ^ { 12 } c ^ { 5 }$ 
C)  $a ^ { 3 } b ^ { 8 } c ^ { 5 }$ 
D)  $a ^ { 2 } b ^ { 12 } c ^ { 6 }$ 
E)  $a ^ { 3 } b ^ { 8 } c ^ { 6 }$ 
A)  $a ^ { 2 } b ^ { 8 } c ^ { 5 }$ 
B)  $a ^ { 3 } b ^ { 12 } c ^ { 5 }$ 
C)  $a ^ { 3 } b ^ { 8 } c ^ { 5 }$ 
D)  $a ^ { 2 } b ^ { 12 } c ^ { 6 }$ 
E)  $a ^ { 3 } b ^ { 8 } c ^ { 6 }$

Question 3

Find the product. $$( y + 4 ) ( y - 4 )$$

Accepted Answer

A)  $y ^ { 2 } - 19$ 
B)  $y ^ { 2 } - 20$ 
C)  $y ^ { 2 } - 16$ 
D)  $y ^ { 2 } - 17$ 
E)  $y ^ { 2 } - 18$ 
A)  $y ^ { 2 } - 19$ 
B)  $y ^ { 2 } - 20$ 
C)  $y ^ { 2 } - 16$ 
D)  $y ^ { 2 } - 17$ 
E)  $y ^ { 2 } - 18$

Question 4

Subtract the bottom polynomial from the top polynomial. $$\begin{array} { c } 
- 5 y ^ { 3 } + 4 y ^ { 2 } - 11 y + 5 \
- 2 y ^ { 3 } - 14 y ^ { 2 } + 17 y - 34\
\hline
\end{array}$$

Accepted Answer

A)  $- 5 y ^ { 3 } - 13 y ^ { 2 } + 21 y - 40$ 
B)  $3 y ^ { 3 } + 18 y ^ { 2 } - 28 y - 39$ 
C)  $- 3 y ^ { 3 } + 18 y ^ { 2 } - 28 y + 39$ 
D)  $- 3 y ^ { 3 } - 18 y ^ { 2 } + 28 y - 41$ 
E)  $- 7 y ^ { 3 } + 10 y ^ { 2 } + 28 y + 36$ 
A)  $- 5 y ^ { 3 } - 13 y ^ { 2 } + 21 y - 40$ 
B)  $3 y ^ { 3 } + 18 y ^ { 2 } - 28 y - 39$ 
C)  $- 3 y ^ { 3 } + 18 y ^ { 2 } - 28 y + 39$ 
D)  $- 3 y ^ { 3 } - 18 y ^ { 2 } + 28 y - 41$ 
E)  $- 7 y ^ { 3 } + 10 y ^ { 2 } + 28 y + 36$

Question 5

Factor completely. $45 x ^ { 7 } - 7 x ^ { 9 } + 10 x ^ { 10 }$

Accepted Answer

A)  $45 x ^ { 7 } - x ^ { 9 } ( 7 + 10 x )$ 
B)  $x ^ { 7 } \left( 45 - 7 x ^ { 2 } \right) + 10 x ^ { 10 }$ 
C)  $x \left( 45 - 7 x ^ { 8 } + 10 x ^ { 9 } \right)$ 
D)  $x ^ { 7 } \left( 45 + 10 x ^ { 3 } \right) - 7 x ^ { 9 }$ 
E)  $x ^ { 7 } \left( 45 - 7 x ^ { 2 } + 10 x ^ { 3 } \right)$ 
A)  $45 x ^ { 7 } - x ^ { 9 } ( 7 + 10 x )$ 
B)  $x ^ { 7 } \left( 45 - 7 x ^ { 2 } \right) + 10 x ^ { 10 }$ 
C)  $x \left( 45 - 7 x ^ { 8 } + 10 x ^ { 9 } \right)$ 
D)  $x ^ { 7 } \left( 45 + 10 x ^ { 3 } \right) - 7 x ^ { 9 }$ 
E)  $x ^ { 7 } \left( 45 - 7 x ^ { 2 } + 10 x ^ { 3 } \right)$

Question 6

Simplify the expression. $$- 4 x y ^ { 2 } ( 3 x + 2 y + 5 z ) - 2 x \left( x y ^ { 2 } - 4 y ^ { 2 } z \right) - 2 y \left( 8 x y ^ { 2 } - 1 \right)$$

Accepted Answer

A)  $- 10 x ^ { 2 } y ^ { 2 } - 28 x y ^ { 2 } z - 24 x y ^ { 3 } + 2 y$ 
B)  $- 14 x ^ { 2 } y ^ { 2 } - 28 x y ^ { 2 } z + 24 x y ^ { 3 } + 2 y$ 
C)  $- 14 x ^ { 2 } y ^ { 2 } - 12 x y ^ { 2 } z - 24 x y ^ { 3 } + 2 y$ 
D)  $- 14 x ^ { 2 } y ^ { 2 } - 28 x y ^ { 2 } z - 24 x y ^ { 3 } + 2 y$ 
E) none of these 
A)  $- 10 x ^ { 2 } y ^ { 2 } - 28 x y ^ { 2 } z - 24 x y ^ { 3 } + 2 y$ 
B)  $- 14 x ^ { 2 } y ^ { 2 } - 28 x y ^ { 2 } z + 24 x y ^ { 3 } + 2 y$ 
C)  $- 14 x ^ { 2 } y ^ { 2 } - 12 x y ^ { 2 } z - 24 x y ^ { 3 } + 2 y$ 
D)  $- 14 x ^ { 2 } y ^ { 2 } - 28 x y ^ { 2 } z - 24 x y ^ { 3 } + 2 y$ 
E) none of these

Question 7

An object has been thrown straight up into the air. The formula $h = v t - 16 t ^ { 2 }$ gives the height h of the object above the ground after t seconds, when it is thrown upward with an initial velocity v . After how many seconds will an object hit the ground if it is thrown with a velocity of 112 feet per second?

Accepted Answer

A)  $t = 18$ sec 
B)  $t = 23$ sec 
C)  $t = 6$ sec 
D)  $t = 20$ sec 
E)  $t = 7$ sec 
A)  $t = 18$ sec 
B)  $t = 23$ sec 
C)  $t = 6$ sec 
D)  $t = 20$ sec 
E)  $t = 7$ sec

Question 8

Determine the degree of the given polynomial. 3 xy + 7 y

Accepted Answer

A) 0 
B) 2 
C) 11 
D) 3 
E) 1 
A) 0 
B) 2 
C) 11 
D) 3 
E) 1

Question 9

Simplify the expression. 3 y ( xy + y )- 9 y 2( x - 2 + 5 y )+ 2( y 3 + y 2)

Accepted Answer

A) - 6 xy 2 + 21 y 2 + 20 y 3 
B) - 6 xy 2 + 23 y 2 - 43 y 3 
C) 12 xy 2 + 21 y 2 - 43 y 3 
D) 6 xy 2 + 21 y 2 - 20 y 3 
E) none of these 
A) - 6 xy 2 + 21 y 2 + 20 y 3 
B) - 6 xy 2 + 23 y 2 - 43 y 3 
C) 12 xy 2 + 21 y 2 - 43 y 3 
D) 6 xy 2 + 21 y 2 - 20 y 3 
E) none of these

Question 10

Factor completely. $6 x ^ { 2 } + 26 x$

Accepted Answer

A)  $2 \left( 3 x ^ { 2 } + 13 x \right)$ 
B)  $3 \left( 2 x ^ { 2 } \right) + 13 ( 2 x )$ 
C)  $3 x ( 2 x ) + 13 ( 2 x )$ 
D)  $x ( 6 x + 26 )$ 
E)  $2 x ( 3 x + 13 )$ 
A)  $2 \left( 3 x ^ { 2 } + 13 x \right)$ 
B)  $3 \left( 2 x ^ { 2 } \right) + 13 ( 2 x )$ 
C)  $3 x ( 2 x ) + 13 ( 2 x )$ 
D)  $x ( 6 x + 26 )$ 
E)  $2 x ( 3 x + 13 )$

Question 11

Factor the expression. $a ^ { 2 } - 4 a + 4$

Accepted Answer

A)  $( a + 2 ) ( a + 2 )$ 
B)  $( a - 2 ) ( a + 2 )$ 
C)  $( a + 4 ) ( a + 1 )$ 
D)  $( a - 2 ) ( a - 2 )$ 
E) prime 
A)  $( a + 2 ) ( a + 2 )$ 
B)  $( a - 2 ) ( a + 2 )$ 
C)  $( a + 4 ) ( a + 1 )$ 
D)  $( a - 2 ) ( a - 2 )$ 
E) prime

Question 12

The area of a triangular sheet of paper is 11 square inches. One side of the triangle is 5 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to the side.

Accepted Answer

A) an altitude of 11 inches, a side of 21 inches long 
B) an altitude of 2 inches, a side of 11 inches long 
C) an altitude of 1 inches, a side of 11 inches long 
D) an altitude of 11 inches, a side of 2 inches long 
E) none of these 
A) an altitude of 11 inches, a side of 21 inches long 
B) an altitude of 2 inches, a side of 11 inches long 
C) an altitude of 1 inches, a side of 11 inches long 
D) an altitude of 11 inches, a side of 2 inches long 
E) none of these

Question 13

Find the product. $( 3 z - 3 t ) ^ { 2 }$

Accepted Answer

A)  $9 z ^ { 2 } - 3 z - 3 t + 9 t ^ { 2 }$ 
B)  $9 z ^ { 2 } - 9 t ^ { 2 }$ 
C)  $9 z ^ { 2 } + 9 t ^ { 2 }$ 
D)  $9 z ^ { 2 } - 18 z t + 9 t ^ { 2 }$ 
E)  $9 z ^ { 2 } - 9 z t + 9 t ^ { 2 }$ 
A)  $9 z ^ { 2 } - 3 z - 3 t + 9 t ^ { 2 }$ 
B)  $9 z ^ { 2 } - 9 t ^ { 2 }$ 
C)  $9 z ^ { 2 } + 9 t ^ { 2 }$ 
D)  $9 z ^ { 2 } - 18 z t + 9 t ^ { 2 }$ 
E)  $9 z ^ { 2 } - 9 z t + 9 t ^ { 2 }$

Question 14

Factor the expression. 8 g - rn - 8 n + rg

Accepted Answer

A) (8 - n )( g + r ) 
B) (8 + n )( g - r ) 
C) ( g - n )(8 + r ) 
D) ( g - n )(8 - r ) 
E) ( g + n )(8 - r ) 
A) (8 - n )( g + r ) 
B) (8 + n )( g - r ) 
C) ( g - n )(8 + r ) 
D) ( g - n )(8 - r ) 
E) ( g + n )(8 - r )

Question 15

The Ortegas have an apple orchard that contains 75 trees. The number of trees in each row is 5 more than twice the number of rows. Find the number of rows and the number of trees per row. __________ rows __________ trees per row

Accepted Answer

The answer of The Ortegas have an apple orchard that...

Question 16

Simplify the expression. $$2 \left( x ^ { 2 } - 7 x - 4 \right) - 3 \left( x ^ { 2 } - 7 x - 4 \right) + 9 \left( x ^ { 2 } - 7 x - 4 \right)$$

Accepted Answer

A)  $8 x ^ { 2 } - 98 x - 56$ 
B)  $8 x ^ { 2 } - 98 x - 32$ 
C)  $8 x ^ { 2 } - 56 x - 32$ 
D)  $8 x ^ { 2 } - 56 x - 56$ 
E) none of these 
A)  $8 x ^ { 2 } - 98 x - 56$ 
B)  $8 x ^ { 2 } - 98 x - 32$ 
C)  $8 x ^ { 2 } - 56 x - 32$ 
D)  $8 x ^ { 2 } - 56 x - 56$ 
E) none of these

Question 17

Find the product. $( 2 a - 4 ) ( 3 a - 3 )$

Accepted Answer

The answer of Find the product. \(( 2 a -...

Question 18

Factor the expression. $$( x - 12 ) ^ { 2 } + ( x - 12 )$$

Accepted Answer

A)  $( x - 12 ) ( x + 11 )$ 
B)  $( x - 14 ) ( x - 11 )$ 
C)  $( x - 12 ) ( x - 13 )$ 
D)  $( x - 12 ) ( x + 13 )$ 
E)  $( x - 12 ) ( x - 11 )$ 
A)  $( x - 12 ) ( x + 11 )$ 
B)  $( x - 14 ) ( x - 11 )$ 
C)  $( x - 12 ) ( x - 13 )$ 
D)  $( x - 12 ) ( x + 13 )$ 
E)  $( x - 12 ) ( x - 11 )$

Question 19

Factor the expression. $x ^ { 2 } + 8 x + 1$

Accepted Answer

A)  $( 3 x + 5 ) ( x + 5 )$ 
B)  $( 2 x + 5 ) ( x + 5 )$ 
C)  $( 2 x + 3 ) ( x - 5 )$ 
D)  $( 2 x - 5 ) ( x + 4 )$ 
E) prime 
A)  $( 3 x + 5 ) ( x + 5 )$ 
B)  $( 2 x + 5 ) ( x + 5 )$ 
C)  $( 2 x + 3 ) ( x - 5 )$ 
D)  $( 2 x - 5 ) ( x + 4 )$ 
E) prime

Question 20

Find two integers whose product is 77 such that one of the integers is three less than twice the other integer.

Accepted Answer

A) 8, 12 
B) 8, 10 
C) 6, 12 
D) 6, 10 
E) 7, 11 
A) 8, 12 
B) 8, 10 
C) 6, 12 
D) 6, 10 
E) 7, 11

Find the product. $\left( 4 s ^ { 6 } z ^ { 6 } \right) \left( 3 s ^ { 4 } z ^ { 3 } \right)$

Raise the monomial to the indicated power. $\left( a b ^ { 6 } c ^ { 3 } \right) ^ { 2 }$

Find the product. $( y + 4 ) ( y - 4 )$

Subtract the bottom polynomial from the top polynomial. -5+4-11y+5 -2-14+17y-34

Factor completely. $45 x ^ { 7 } - 7 x ^ { 9 } + 10 x ^ { 10 }$

Simplify the expression. $- 4 x y ^ { 2 } ( 3 x + 2 y + 5 z ) - 2 x \left( x y ^ { 2 } - 4 y ^ { 2 } z \right) - 2 y \left( 8 x y ^ { 2 } - 1 \right)$

Determine the degree of the given polynomial. 3 xy + 7 y

Simplify the expression. 3 y ( xy + y )- 9 y²( x - 2 + 5 y )+ 2( y³+ y²)

Factor completely. $6 x ^ { 2 } + 26 x$

Factor the expression. $a ^ { 2 } - 4 a + 4$

The area of a triangular sheet of paper is 11 square inches. One side of the triangle is 5 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to the side.

Find the product. $( 3 z - 3 t ) ^ { 2 }$

Factor the expression. 8 g - rn - 8 n + rg

The Ortegas have an apple orchard that contains 75 trees. The number of trees in each row is 5 more than twice the number of rows. Find the number of rows and the number of trees per row. rows trees per row

Simplify the expression. $2 \left( x ^ { 2 } - 7 x - 4 \right) - 3 \left( x ^ { 2 } - 7 x - 4 \right) + 9 \left( x ^ { 2 } - 7 x - 4 \right)$

Find the product. $( 2 a - 4 ) ( 3 a - 3 )$

Factor the expression. $( x - 12 ) ^ { 2 } + ( x - 12 )$

Factor the expression. $x ^ { 2 } + 8 x + 1$

Find two integers whose product is 77 such that one of the integers is three less than twice the other integer.

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

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Exam 3: Polynomials

Find the product. (4s6z6)(3s4z3)\left( 4 s ^ { 6 } z ^ { 6 } \right) \left( 3 s ^ { 4 } z ^ { 3 } \right)(4s6z6)(3s4z3)

Raise the monomial to the indicated power. (ab6c3)2\left( a b ^ { 6 } c ^ { 3 } \right) ^ { 2 }(ab6c3)2

Find the product. (y+4)(y−4)( y + 4 ) ( y - 4 )(y+4)(y−4)

Subtract the bottom polynomial from the top polynomial. -5+4-11y+5 -2-14+17y-34

Factor completely. 45x7−7x9+10x1045 x ^ { 7 } - 7 x ^ { 9 } + 10 x ^ { 10 }45x7−7x9+10x10

Simplify the expression. −4xy2(3x+2y+5z)−2x(xy2−4y2z)−2y(8xy2−1)- 4 x y ^ { 2 } ( 3 x + 2 y + 5 z ) - 2 x \left( x y ^ { 2 } - 4 y ^ { 2 } z \right) - 2 y \left( 8 x y ^ { 2 } - 1 \right)−4xy2(3x+2y+5z)−2x(xy2−4y2z)−2y(8xy2−1)

Determine the degree of the given polynomial. 3 xy + 7 y

Simplify the expression. 3 y ( xy + y )- 9 y 2( x - 2 + 5 y )+ 2( y 3 + y 2)

Factor completely. 6x2+26x6 x ^ { 2 } + 26 x6x2+26x

Factor the expression. a2−4a+4a ^ { 2 } - 4 a + 4a2−4a+4

The area of a triangular sheet of paper is 11 square inches. One side of the triangle is 5 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to the side.

Find the product. (3z−3t)2( 3 z - 3 t ) ^ { 2 }(3z−3t)2

Factor the expression. 8 g - rn - 8 n + rg

The Ortegas have an apple orchard that contains 75 trees. The number of trees in each row is 5 more than twice the number of rows. Find the number of rows and the number of trees per row. __________ rows __________ trees per row

Simplify the expression. 2(x2−7x−4)−3(x2−7x−4)+9(x2−7x−4)2 \left( x ^ { 2 } - 7 x - 4 \right) - 3 \left( x ^ { 2 } - 7 x - 4 \right) + 9 \left( x ^ { 2 } - 7 x - 4 \right)2(x2−7x−4)−3(x2−7x−4)+9(x2−7x−4)

Find the product. (2a−4)(3a−3)( 2 a - 4 ) ( 3 a - 3 )(2a−4)(3a−3)

Factor the expression. (x−12)2+(x−12)( x - 12 ) ^ { 2 } + ( x - 12 )(x−12)2+(x−12)

Factor the expression. x2+8x+1x ^ { 2 } + 8 x + 1x2+8x+1

Find two integers whose product is 77 such that one of the integers is three less than twice the other integer.

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Find the product. $\left( 4 s ^ { 6 } z ^ { 6 } \right) \left( 3 s ^ { 4 } z ^ { 3 } \right)$

Raise the monomial to the indicated power. $\left( a b ^ { 6 } c ^ { 3 } \right) ^ { 2 }$

Find the product. $( y + 4 ) ( y - 4 )$

Factor completely. $45 x ^ { 7 } - 7 x ^ { 9 } + 10 x ^ { 10 }$

Simplify the expression. $- 4 x y ^ { 2 } ( 3 x + 2 y + 5 z ) - 2 x \left( x y ^ { 2 } - 4 y ^ { 2 } z \right) - 2 y \left( 8 x y ^ { 2 } - 1 \right)$

Simplify the expression. 3 y ( xy + y )- 9 y²( x - 2 + 5 y )+ 2( y³+ y²)

Factor completely. $6 x ^ { 2 } + 26 x$

Factor the expression. $a ^ { 2 } - 4 a + 4$

Find the product. $( 3 z - 3 t ) ^ { 2 }$

The Ortegas have an apple orchard that contains 75 trees. The number of trees in each row is 5 more than twice the number of rows. Find the number of rows and the number of trees per row. rows trees per row

Simplify the expression. $2 \left( x ^ { 2 } - 7 x - 4 \right) - 3 \left( x ^ { 2 } - 7 x - 4 \right) + 9 \left( x ^ { 2 } - 7 x - 4 \right)$

Find the product. $( 2 a - 4 ) ( 3 a - 3 )$

Factor the expression. $( x - 12 ) ^ { 2 } + ( x - 12 )$

Factor the expression. $x ^ { 2 } + 8 x + 1$