Polynomials — Test Answers

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Let A , b , and c be real numbers where A is not equal to b is not equal to c is not equal to 0 Which of the following functions could represent the graph?

f of x is equal to x cubed open paren x minus A close paren cubed open paren x minus b close paren open paren x minus c close paren squared

f of x is equal to x squared open paren x minus A close paren squared open paren x minus b close paren to the 4th power open paren x minus c close paren

f of x is equal to open paren x minus A close paren squared times open paren x minus b close paren times open paren x minus c close paren to the 6th power

f of x is equal to x to the 4th power open paren x minus A close paren open paren x minus b close paren cubed open paren x minus c close paren cubed

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Which polynomial function has a leading coefficient of 2 , root negative 4 with multiplicity 3 , and root 10 with multiplicity 1 ?

f of x is equal to 2 open paren x plus 4 close paren open paren x plus 4 close paren open paren x plus 4 close paren open paren x minus 10 close paren

f of x is equal to 3 open paren x minus 4 close paren open paren x minus 4 close paren open paren x plus 10 close paren

f of x is equal to 3 open paren x plus 4 close paren open paren x plus 4 close paren open paren x minus 10 close paren

f of x is equal to 2 open paren x minus 4 close paren open paren x minus 4 close paren open paren x minus 4 close paren open paren x plus 10 close paren

Use synthetic division to solve open paren x to the 4th power minus 1 close paren divided by open paren x minus 1 close paren What is the quotient?

x cubed

x cubed minus x squared plus x minus 1

x cubed plus x squared plus x plus 1

x cubed minus 2

What is the remainder when (x^4+36) is divided by (x^2−8) ?

100

117

According to the Rational Root Theorem, what are all the potential rational roots of f of x is equal to 5 x cubed minus 7 x plus 11 ?

plus or minus 1 over 11 , plus or minus 1 fifth , plus or minus 5 over 11 , plus or minus 1 , plus or minus 11 fifths , plus or minus 5 , plus or minus 11

0 , plus or minus 1 over 11 , plus or minus 1 fifth , plus or minus 5 over 11 , plus or minus 1 , plus or minus 11 fifths , plus or minus 5 , plus or minus 11

plus or minus 1 over 11 , plus or minus 5 over 11 , plus or minus 1 , plus or minus 5

plus or minus 1 fifth , plus or minus 1 , plus or minus 11 fifths , plus or minus 11

According to the Rational Root Theorem, which is a factor of the polynomial f of x is equal to 3 x cubed minus 5 x squared minus 12 x plus 20 ?

3 x minus 5

2 x minus 1

3 x plus 5

2 x plus 1

Which statement best describes the equation open paren x plus 5 close paren squared plus 4 times open paren x plus 5 close paren plus 12 is equal to 0 ?

The equation is quadratic in form because it can be rewritten as a quadratic equation with u substitution u is equal to open paren x plus 5 close paren .

The equation is quadratic in form because when it is expanded, it is a fourth-degree polynomial.

The equation is not quadratic in form because it cannot be solved by using the quadratic formula.

The equation is not quadratic in form because there is no real solution.

What are the roots of the polynomial equation x cubed minus 7 x is equal to 6 x minus 12 ? Use a graphing calculator and a system of equations.

negative 4 , 1 , 3

negative 3 , negative 1 , 4

negative 6 , 6

1 , 3

Which expression is a sum of cubes?

64 x to the 6th power y to the 12th power plus 125 x to the 9th power y cubed

negative 64 x to the 6th power y to the 12th power plus 125 x to the 16th power y cubed

negative 32 x to the 6th power y to the 12th power plus 125 x to the 16th power y cubed

32 x to the 6th power y to the 12th power plus 125 x to the 9th power y cubed

What is the fifth term in the binomial expansion of open paren x plus 5 close paren to the 8th power ?

43 comma 750 x to the 4th power

7 comma 000 x to the 5th power

175 comma 000 x cubed

3 comma 125 x to the 5th power

What is the quotient of open paren x cubed minus 3 x squared plus 3 x minus 2 close paren divided by open paren x squared minus x plus 1 close paren ?

x minus 2

x plus 2

x plus 1

x minus 4

Which table describes the behavior of the graph of f of x is equal to 2 x cubed minus 26 x minus 24 ?

Table with 2 columns and 5 rows.Row 1: Column 1, 'Interval'; Column 2, 'Relation of graph to x-axis' Row 2: Column 1, 'open paren negative infinity comma negative 4 close paren'; Column 2, 'Above' Row 3: Column 1, '(−4, 1)'; Column 2, 'Below' Row 4: Column 1, '(1, 3)'; Column 2, 'Above' Row 5: Column 1, '(3, ∞)'; Column 2, 'Below'

Table with 2 columns and 5 rows.Row 1: Column 1, 'Interval'; Column 2, 'Relation of graph to x-axis' Row 2: Column 1, 'open paren negative infinity comma negative 3 close paren'; Column 2, 'Below' Row 3: Column 1, 'open paren negative 3 comma negative 1 close paren'; Column 2, 'Above' Row 4: Column 1, '(−1, 4)'; Column 2, 'Below' Row 5: Column 1, '(4, ∞)'; Column 2, 'Above'

Table with 2 columns and 5 rows.Row 1: Column 1, 'Interval'; Column 2, 'Relation of graph to x-axis' Row 2: Column 1, 'open paren negative infinity comma negative 3 close paren'; Column 2, 'Above' Row 3: Column 1, 'open paren negative 3 comma negative 1 close paren'; Column 2, 'Below' Row 4: Column 1, '(−1, 4)'; Column 2, 'Above' Row 5: Column 1, '(4, ∞)'; Column 2, 'Below'

Table with 2 columns and 5 rows.Row 1: Column 1, 'Interval'; Column 2, 'Relation of graph to x-axis' Row 2: Column 1, 'open paren negative infinity comma negative 4 close paren'; Column 2, 'Below' Row 3: Column 1, '(−4, 1)'; Column 2, 'Above' Row 4: Column 1, '(1, 3)'; Column 2, 'Below' Row 5: Column 1, '(3, ∞)'; Column 2, 'Above'

What is the cube root of negative 1 comma 000 p to the 12th power q cubed ?

10 p to the 4th power

negative 10 p to the 4th power q

10 p to the 4th power q

negative 10 p to the 4th power

Which equation is quadratic in form?

5 x to the 6th power plus x to the 4th power plus 12 is equal to 0

x to the 9th power plus x cubed minus 10 is equal to 0

3 x to the 5th power plus 8 x cubed plus 6 is equal to 0

6 x to the 4th power plus 7 x squared minus 3 is equal to 0

Which expression is equivalent to open paren 4 y squared close paren cubed times open paren 3 y squared close paren ?

12 y to the 8th power

12 y to the 12th power

192 y to the 8th power

192 y to the 12th power

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 correct because all solutions are intersection points of the graphs.

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

She is correct because the solutions are irrational.

What is the sum of the first seven terms of the geometric series? 3 plus 12 plus 48 plus 192 plus dot dot dot

65 comma 535

4 comma 372

12 comma 288

16 comma 383

Which expression is equivalent to open paren 5 x cubed close paren times 4 x cubed ?

20 x to the 6th power

320 x to the 6th power

8 comma 000 x to the 6th power

500 x to the 6th power

The price that a company charged for a basketball hoop is given by the equation 50 minus 5 x squared where x is the number of hoops that are produced, in millions. It costs the company 30 dollars to make each basketball hoop. The company recently reduced its production to 1 million hoops but maintained its profit of 15 million dollars. Approximately how many basketball hoops did the company previously produce to make the same profit?

1 point 3 million hoops

15 million hoops

30 million hoops

1 point 4 million hoops

Which polynomial function has a leading coefficient of 1 , roots negative 2 and 7 with multiplicity 1 , and root 5 with multiplicity 2 ?

f of x is equal to 2 open paren x plus 7 close paren open paren x plus 5 close paren open paren x minus 2 close paren

f of x is equal to open paren x minus 7 close paren times open paren x minus 5 close paren times open paren x minus 5 close paren times open paren x plus 2 close paren

f of x is equal to 2 open paren x minus 7 close paren open paren x minus 5 close paren open paren x plus 2 close paren

f of x is equal to open paren x plus 7 close paren times open paren x plus 5 close paren times open paren x plus 5 close paren times open paren x minus 2 close paren

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Polynomials — Test Answers

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