Question 1

Simplify. (A ssume all variables are nonzero.) 
- (13x) 0(13 \mathrm{x}) ^{0}(13x) 0

Accepted Answer

A)   13
B)    13x13 x13x 
C)   0
D)   1

Question 2

Factor completely. If the polynomial cannot be factored, write "prime."
- 3x5+9x4y−30x3y23 x^{5}+9 x^{4} y-30 x^{3} y^{2}3x5+9x4y−30x3y2

Accepted Answer

A)    (3x2+6xy) (x3−5y) \left(3 x^{2}+6 x y\right) \left(x^{3}-5 y\right) (3x2+6xy) (x3−5y)  
B)    (x−2y) (3x4+15xy) (x-2 y) \left(3 x^{4}+15 x y\right) (x−2y) (3x4+15xy)  
C)    3x3(x+2y) (x−5y) 3 x^{3}(x+2 y) (x-5 y) 3x3(x+2y) (x−5y)  
D)    3x3(x−2y) (x+5y) 3 x^{3}(x-2 y) (x+5 y) 3x3(x−2y) (x+5y)

Question 3

Factor completely. If the polynomial cannot be factored, write "prime."
- 15x3−2x2−8x15 x^{3}-2 x^{2}-8 x15x3−2x2−8x

Accepted Answer

A)    x(3x+2) (5x−4) x(3 x+2) (5 x-4) x(3x+2) (5x−4)  
B)    (3x−2) (5x+4) (3 x-2) (5 x+4) (3x−2) (5x+4)  
C)    x(15x+1) (x−8) x(15 x+1) (x-8) x(15x+1) (x−8)  
D)    (x2−4) (15x+2) \left(x^{2}-4\right) (15 x+2) (x2−4) (15x+2)

Question 4

Factor the GCF out of the given expression.
- 9x(x−4) +(x−4) 9 x(x-4) +(x-4) 9x(x−4) +(x−4)

Accepted Answer

A)    (9x−4) (x+1) (9 x-4) (x+1) (9x−4) (x+1)  
B)    (9x+1) (x−4) (9 x+1) (x-4) (9x+1) (x−4)  
C)    9x(x−4) 9 x(x-4) 9x(x−4)  
D)    (9x+4) (x+1) (9 x+4) (x+1) (9x+4) (x+1)

Question 5

Divide using long division.
- x2+7x+7x+3\frac{x^{2}+7 x+7}{x+3}x+3x2+7x+7​

Accepted Answer

A)    x+4+5x+3x+4+\frac{5}{x+3}x+4+x+35​ 
B)    x+4x+3\frac{x+4}{x+3}x+3x+4​ 
C)    x+4−5x+3x+4-\frac{5}{x+3}x+4−x+35​ 
D)    x+5x+5x+5

Question 6

Factor completely. If the polynomial cannot be factored, write "prime."
- x3−1000x^{3}-1000x3−1000

Accepted Answer

A)    (x−10) (x2+100) (x-10) \left(x^{2}+100\right) (x−10) (x2+100)  
B)    (x+10) (x2−10x+100) (\mathrm{x}+10) \left(\mathrm{x}^{2}-10 \mathrm{x}+100\right) (x+10) (x2−10x+100)  
C)    (x−10) (x2+10x+100) (x-10) \left(x^{2}+10 x+100\right) (x−10) (x2+10x+100)  
D)    (x+1000) (x2−1) (x+1000) \left(x^{2}-1\right) (x+1000) (x2−1)

Question 7

Convert the given number to scientific notation
- 1,054,000,000,000,000,0001,054,000,000,000,000,0001,054,000,000,000,000,000

Accepted Answer

A)    1.054×10−181.054 	imes 10^{-18}1.054×10−18 
B)    1054×10151054 	imes 10^{15}1054×1015 
C)    1.054×10181.054 	imes 10^{18}1.054×1018 
D)    1054×10−151054 	imes 10^{-15}1054×10−15

Question 8

Determine whether the simplified version of the given expression would be a
- (x−5) (x2+5x+25) (x-5) \left(x^{2}+5 x+25\right) (x−5) (x2+5x+25)

Accepted Answer

A)   trinomial
B)   binomial
C)   polynomial with four or more terms

Question 9

−5x3z4⋅2x4z2-5 x^{3} z^{4} \cdot 2 x^{4} z^{2}−5x3z4⋅2x4z2

Accepted Answer

A)    −10xz7-10 \mathrm{xz}^{7}−10xz7 
B)    −10x6z7-10 x ^6{z} ^7−10x6z7 
C)    −10x7z6-10 x^{7} z^{6}−10x7z6 
D)    −10xz6-10 x z 6−10xz6

Question 10

Evaluate the polynomial
- x2+3y2+2xyx^{2}+3 y^{2}+2 x yx2+3y2+2xy  for  x=5x=5x=5  and  y=3y=3y=3

Accepted Answer

A)   52
B)   82
C)   97
D)   55

Question 11

Factor completely. If the polynomial cannot be factored, write "prime."
- 2x2+2xy−40y22 x^{2}+2 x y-40 y^{2}2x2+2xy−40y2

Accepted Answer

A)    (x−4y) (2x+10y) (x-4 y) (2 x+10 y) (x−4y) (2x+10y)  
B)    2(x−4y) (x+5y) 2(x-4 y) (x+5 y) 2(x−4y) (x+5y)  
C)    2(x+4y) (x−5y) 2(x+4 y) (x-5 y) 2(x+4y) (x−5y)  
D)    (2x+8y) (x−5y) (2 x+8 y) (x-5 y) (2x+8y) (x−5y)

Question 12

Divide using long division.
- 3x2+19x+20x+4\frac{3 x^{2}+19 x+20}{x+4}x+43x2+19x+20​

Accepted Answer

A)    3x+7−8x+43 x+7-\frac{8}{x+4}3x+7−x+48​ 
B)    3x+7+8x+43 x+7+\frac{8}{x+4}3x+7+x+48​ 
C)    3x−7−8x+43 x-7-\frac{8}{x+4}3x−7−x+48​ 
D)    3x+73 x+73x+7

Question 13

Factor completely. If the polynomial cannot be factored, write "prime."
- x2−16x+64x^{2}-16 x+64x2−16x+64

Accepted Answer

A)    (x−4) 2(x-4) ^{2}(x−4) 2 
B)    (x+8) 2(x+8) ^{2}(x+8) 2 
C)    (x−8) 2(x-8) ^{2}(x−8) 2 
D)   prime

Question 14

Factor completely. If the polynomial cannot be factored, write "prime."
- 16x2−8x+116 x^{2}-8 x+116x2−8x+1

Accepted Answer

A)    (4x−1) 2(4 x-1) ^{2}(4x−1) 2 
B)    (x+4) 2(x+4) ^{2}(x+4) 2 
C)    (4x+1) 2(4 x+1) ^{2}(4x+1) 2 
D)   prime

Question 15

A rectangular garden has dimensions of 18 feet by 15 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 234 square feet?

Accepted Answer

A)   5.5 feet
B)   5 feet
C)   4 feet
D)   3 feet

Question 16

Find the missing monomial, factor or term.
- (?) 2=x2+16x+64(?) ^{2}=x^{2}+16 x+64(?) 2=x2+16x+64

Accepted Answer

A)    x2+8x^{2}+8x2+8 
B)    x+8x+8x+8 
C)    x−8x-8x−8 
D)    −x+8-x+8−x+8

Question 17

Factor completely. If the polynomial cannot be factored, write "prime."
- 60x6+39x4+6x260 x^{6}+39 x^{4}+6 x^{2}60x6+39x4+6x2

Accepted Answer

A)    (12x3+3) (5x3+2) \left(12 x^{3}+3\right) \left(5 x^{3}+2\right) (12x3+3) (5x3+2)  
B)    3x2(5x2−2) (4x2−1) 3 x^{2}\left(5 x^{2}-2\right) \left(4 x^{2}-1\right) 3x2(5x2−2) (4x2−1)  
C)    3(4x4+1) (5x2+2) 3\left(4 x^{4}+1\right) \left(5 x^{2}+2\right) 3(4x4+1) (5x2+2)  
D)    3x2(4x2+1) (5x2+2) 3 x^{2}\left(4 x^{2}+1\right) \left(5 x^{2}+2\right) 3x2(4x2+1) (5x2+2)

Question 18

Factor completely. If the polynomial cannot be factored, write "prime."
- 8x3−216y38 x^{3}-216 y^{3}8x3−216y3

Accepted Answer

A)    8(x−3y) (x2+9y2) 8(x-3 y) \left(x^{2}+9 y^{2}\right) 8(x−3y) (x2+9y2)  
B)    8(x−3y) (x2+3xy+9y2) 8(x-3 y) \left(x^{2}+3 x y+9 y^{2}\right) 8(x−3y) (x2+3xy+9y2)  
C)    8(x+3y) (x2−3xy+9y2) 8(x+3 y) \left(x^{2}-3 x y+9 y^{2}\right) 8(x+3y) (x2−3xy+9y2)  
D)    (8x−3y) (x2+3y+72y2) (8 x-3 y) \left(x^{2}+3 y+72 y^{2}\right) (8x−3y) (x2+3y+72y2)

Question 19

Find the missing factor or exponent(s) .
- (x10y7z8) ?=x50y35z40\left(\frac{x^{10} y^{7}}{z^{8}}\right) ^{?}=\frac{x^{50} y^{35}}{z^{40}}(z8x10y7​) ?=z40x50y35​

Accepted Answer

A)   7
B)   8
C)   10
D)   5

Question 20

Perform the indicated calculation. Express your answer using scientific notation.
- (1.1×10−5) (1.5×10−8) \left(1.1 	imes 10^{-5}ight) \left(1.5 	imes 10^{-8}ight) (1.1×10−5) (1.5×10−8)

Accepted Answer

A)    1.65×10131.65 	imes 10^{13}1.65×1013 
B)    1.65×10−131.65 	imes 10^{-13}1.65×10−13 
C)    1.65×10−31.65 	imes 10^{-3}1.65×10−3 
D)    2.6×10132.6 	imes 10^{13}2.6×1013

Exam 5: Exponents, Polynomials, and Factoring Polynomials

Factor completely. If the polynomial cannot be factored, write "prime." - x3−1000x^{3}-1000x3−1000

Correct AnswerverifiedShow Answer

Find the missing factor or exponent(s) . - (x10y7z8) ?=x50y35z40\left(\frac{x^{10} y^{7}}{z^{8}}\right) ^{?}=\frac{x^{50} y^{35}}{z^{40}}(z8x10y7​) ?=z40x50y35​

Correct AnswerverifiedShow Answer

Factor completely. If the polynomial cannot be factored, write "prime." - 15x3−2x2−8x15 x^{3}-2 x^{2}-8 x15x3−2x2−8x

Correct AnswerverifiedShow Answer

Factor completely. If the polynomial cannot be factored, write "prime." - 8x3−216y38 x^{3}-216 y^{3}8x3−216y3

Correct AnswerverifiedShow Answer

Convert the given number to scientific notation - 1,054,000,000,000,000,0001,054,000,000,000,000,0001,054,000,000,000,000,000

Correct AnswerverifiedShow Answer

Factor completely. If the polynomial cannot be factored, write "prime." - 60x6+39x4+6x260 x^{6}+39 x^{4}+6 x^{2}60x6+39x4+6x2

Correct AnswerverifiedShow Answer

Factor completely. If the polynomial cannot be factored, write "prime." - 3x5+9x4y−30x3y23 x^{5}+9 x^{4} y-30 x^{3} y^{2}3x5+9x4y−30x3y2

Correct AnswerverifiedShow Answer

Factor completely. If the polynomial cannot be factored, write "prime." - x2−16x+64x^{2}-16 x+64x2−16x+64

Correct AnswerverifiedShow Answer

−5x3z4⋅2x4z2-5 x^{3} z^{4} \cdot 2 x^{4} z^{2}−5x3z4⋅2x4z2

Correct AnswerverifiedShow Answer

Factor completely. If the polynomial cannot be factored, write "prime." - 16x2−8x+116 x^{2}-8 x+116x2−8x+1

Correct AnswerverifiedShow Answer

Find the missing monomial, factor or term. - (?) 2=x2+16x+64(?) ^{2}=x^{2}+16 x+64(?) 2=x2+16x+64

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Perform the indicated calculation. Express your answer using scientific notation. - (1.1×10−5) (1.5×10−8) \left(1.1 \times 10^{-5}\right) \left(1.5 \times 10^{-8}\right) (1.1×10−5) (1.5×10−8)

Correct AnswerverifiedShow Answer

Divide using long division. - x2+7x+7x+3\frac{x^{2}+7 x+7}{x+3}x+3x2+7x+7​

Correct AnswerverifiedShow Answer

Evaluate the polynomial - x2+3y2+2xyx^{2}+3 y^{2}+2 x yx2+3y2+2xy for x=5x=5x=5 and y=3y=3y=3

Correct AnswerverifiedShow Answer

Divide using long division. - 3x2+19x+20x+4\frac{3 x^{2}+19 x+20}{x+4}x+43x2+19x+20​

Correct AnswerverifiedShow Answer

A rectangular garden has dimensions of 18 feet by 15 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 234 square feet?

Correct AnswerverifiedShow Answer

Factor the GCF out of the given expression. - 9x(x−4) +(x−4) 9 x(x-4) +(x-4) 9x(x−4) +(x−4)

Correct AnswerverifiedShow Answer

Factor completely. If the polynomial cannot be factored, write "prime." - 2x2+2xy−40y22 x^{2}+2 x y-40 y^{2}2x2+2xy−40y2

Correct AnswerverifiedShow Answer

Simplify. (A ssume all variables are nonzero.) - (13x) 0(13 \mathrm{x}) ^{0}(13x) 0

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Determine whether the simplified version of the given expression would be a - (x−5) (x2+5x+25) (x-5) \left(x^{2}+5 x+25\right) (x−5) (x2+5x+25)

Correct AnswerverifiedShow Answer

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}-1000$

Correct Answer
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Find the missing factor or exponent(s) . - $\left(\frac{x^{10} y^{7}}{z^{8}}\right) ^{?}=\frac{x^{50} y^{35}}{z^{40}}$

Correct Answer
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Factor completely. If the polynomial cannot be factored, write "prime." - $15 x^{3}-2 x^{2}-8 x$

Correct Answer
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Factor completely. If the polynomial cannot be factored, write "prime." - $8 x^{3}-216 y^{3}$

Correct Answer
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Convert the given number to scientific notation - $1,054,000,000,000,000,000$

Correct Answer
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Factor completely. If the polynomial cannot be factored, write "prime." - $60 x^{6}+39 x^{4}+6 x^{2}$

Correct Answer
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Factor completely. If the polynomial cannot be factored, write "prime." - $3 x^{5}+9 x^{4} y-30 x^{3} y^{2}$

Correct Answer
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Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-16 x+64$

Correct Answer
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$-5 x^{3} z^{4} \cdot 2 x^{4} z^{2}$

Correct Answer
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Factor completely. If the polynomial cannot be factored, write "prime." - $16 x^{2}-8 x+1$

Correct Answer
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Find the missing monomial, factor or term. - $(?) ^{2}=x^{2}+16 x+64$

Correct Answer
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Perform the indicated calculation. Express your answer using scientific notation. - $\left(1.1 \times 10^{-5}\right) \left(1.5 \times 10^{-8}\right)$

Correct Answer
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Divide using long division. - $\frac{x^{2}+7 x+7}{x+3}$

Correct Answer
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Evaluate the polynomial - $x^{2}+3 y^{2}+2 x y$ for $x=5$ and $y=3$

Correct Answer
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Divide using long division. - $\frac{3 x^{2}+19 x+20}{x+4}$

Correct Answer
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Correct Answer
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Factor the GCF out of the given expression. - $9 x(x-4) +(x-4)$

Correct Answer
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Factor completely. If the polynomial cannot be factored, write "prime." - $2 x^{2}+2 x y-40 y^{2}$

Correct Answer
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Simplify. (A ssume all variables are nonzero.) - $(13 \mathrm{x}) ^{0}$

Correct Answer
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Determine whether the simplified version of the given expression would be a - $(x-5) \left(x^{2}+5 x+25\right)$

Correct Answer
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