Answers KISD SS-3401A-Precalculus Honors ARational Inequalities

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Which expression represents the correct form for the quotient and remainder, written as partial fractions, of ?

A + StartFraction B Over x + 3 EndFraction + StartFraction C Over 2 x minus 7 EndFraction

A + StartFraction B x + C Over x + 3 EndFraction + StartFraction D x + E Over 2 x minus 7 EndFraction

A x + B + StartFraction C Over x + 3 EndFraction + StartFraction D Over 2 x minus 7 EndFraction

A x + B + StartFraction C x + D Over x + 3 EndFraction + StartFraction E x + F Over 2 x minus 7 EndFraction

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What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

–6, 6

–4, 1, 3

–3, –1, 4

1, 3

Review the work showing the first few steps in writing a partial fraction decomposition.x3 + 8x – 3 = (Ax + B)(x2 + 5) + Cx + Dx3 + 8x – 3 = Ax3 + 5Ax + Bx2 + 5B + Cx + D

A = 0; B = 1; C = –3; D = 3

A = 0; B = 1; C = 3; D = –3

A = 1; B = 0; C = –3; D = 3

A = 1; B = 0; C = 3; D = –3

What is the solution to x 3 + 4x 2 > x + 4?

–4 < x < –1

–4 < x < 1

–4 < x < –1 or x > 1

x < –4 or –1 < x < 1

What is the solution of ?

or x > 4

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Carlos graphed the system of equations that can be used to solve .What are the roots of the polynomial equation?

–3, –2, 3

–3, 2

18, 32

18, 32, 66

How many integers satisfy the inequality (x 2 – 4)(x 2 – 10) < 0?

none

two

four

an infinite number

What is the solution of ?

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The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

She is incorrect because systems may have only complex solutions which are not visible on a graph.

She is incorrect because the solutions may have multiplicity greater than 1.

She is correct because all solutions are intersection points of the graphs.

She is correct because the solutions are irrational.

What is the solution set of ?

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Mario makes 6 free throw shots out of his first 10 attempts. What is the least number of consecutive shots Mario must make to increase his overall percentage from 60% to at least 70%?

1 shot

4 shots

10 shots

14 shots

The square root of a number is greater than the square of the number. For what set of numbers is this true?

(0, 1)

[0, 1]

[1, ꝏ)

(1, ꝏ)

What is the correct form of the partial fraction decomposition for ?

StartFraction A Over x + 2 EndFraction + StartFraction B Over (x + 2) squared EndFraction

StartFraction A Over x + 2 EndFraction + StartFraction B x + C Over (x + 2) squared EndFraction

StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C Over (x + 2) squared EndFraction

StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C x + D Over (x + 2) squared EndFraction

What is the solution to (x – 3)3(x + 1)(x – 2) ≤ 0?

(–ꝏ, –1) U (2, 3)

(–ꝏ, –1] U [2, 3]

(–1, 2) U (3, ꝏ)

[–1, 2] U [3, ꝏ)

What is the partial fraction decomposition of ?

StartFraction 1 Over 3 x EndFraction + StartFraction x minus 2 Over 4 x squared + 9 EndFraction

StartFraction 1 Over 3 x EndFraction + StartFraction x + 2 Over 4 x squared + 9 EndFraction

StartFraction negative 2 Over 3 x EndFraction + StartFraction x minus 1 Over 4 x squared + 9 EndFraction

StartFraction negative 2 Over 3 x EndFraction + StartFraction x + 1 Over 4 x squared + 9 EndFraction

A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.

4 inches

5 inches

9 inches

10 inches

What is the solution of ?

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Review the work showing the first few steps in writing a partial fraction decomposition.4x + 40 = A(x + 6) + B(x + 2)4x + 40 = Ax + 6A + Bx + 2B

StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction negative 12 Over x + 2 EndFraction + StartFraction 16 Over x + 6 EndFraction

StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction negative 4 Over x + 2 EndFraction + StartFraction 8 Over x + 6 EndFraction

StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 8 Over x + 2 EndFraction + StartFraction negative 4 Over x + 6 EndFraction

StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 16 Over x + 2 EndFraction + StartFraction negative 12 Over x + 6 EndFraction

What is the quotient and remainder, written as partial fractions, of ?

5 + StartFraction 10 Over x minus 1 EndFraction + StartFraction 3 Over 3 x + 8 EndFraction

5 + StartFraction 10 Over x minus 1 EndFraction minus StartFraction 3 Over 3 x + 8 EndFraction

5 minus StartFraction 10 Over x minus 1 EndFraction + StartFraction 3 Over 3 x + 8 EndFraction

5 minus StartFraction 10 Over x minus 1 EndFraction minus StartFraction 3 Over 3 x + 8 EndFraction

What is the correct form of the partial fraction decomposition for the expression ?

StartFraction A Over x squared + StartFraction B Over 9 x EndFraction

StartFraction A Over x EndFraction + StartFraction B Over x + 9 EndFraction

StartFraction A x + B Over x squared EndFraction + StartFraction C Over 9 x EndFraction

StartFraction A x + B Over x EndFraction + StartFraction C Over x + 9 EndFraction

Which graph shows the solution set of ?

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What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations. Round noninteger roots to the nearest hundredth.

–12, 20

–2.73, 2, 2.73

–1.73, 1.73, 2

–20, 12

What is the partial fraction decomposition of ?

StartFraction 6 x + 17 Over (x + 1) squared EndFraction = StartFraction 6 Over x + 1 EndFraction + StartFraction 11 Over (x + 1) squared EndFraction

SStartFraction 6 x + 17 Over (x + 1) squared EndFraction = StartFraction 6 Over x + 1 EndFraction + StartFraction 17 Over (x + 1) squared EndFraction

StartFraction 6 x + 17 Over (x + 1) squared EndFraction = StartFraction 6 Over x + 1 EndFraction + StartFraction 11 Over (x + 1) squared EndFraction

StartFraction 6 x + 17 Over (x + 1) squared EndFraction = StartFraction 6 Over x + 1 EndFraction minus StartFraction 17 Over (x + 1) squared EndFraction

What is the solution to (x + 2)(x – 3)2 > 0?

A number line going from negative 4 to 4. The entire line is shaded with arrows going left and right.

A number line going from negative 4 to 4. An open circle is at negative 2. The line is shaded to the right of negative 2.

A number line going from negative 4 to 4. Open circles are at negative 2 and 3. The line is shaded between negative 2 and 3.

A number line going from negative 4 to 4. Open circles are at negative 2 and 3. The line is shaded to the right of negative 2.

Review the work showing the first few steps in writing a partial fraction decomposition.2x2 + 15x + 19 = A(x + 4)2 + B(x + 4) + C2x2 + 15x + 19 = Ax2 + 8Ax + 16A + Bx + 4B + C

Option

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