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If open paren x minus 5 close paren is a factor of f of x , which of the following must be true?

A root of f of x is x is equal to 5 .

A root of f of x is x is equal to negative 5 .

Both x is equal to negative 5 and x is equal to 5 are roots of f of x .

Neither x is equal to negative 5 nor x is equal to 5 is a root of f of x .

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The polynomial function f of x is equal to 3 x to the 5th power minus 2 x squared plus 7 x models the motion of a roller coaster. The roots of the function represent when the roller coaster is at ground level. Which answer choice represents all potential values of when the roller coaster is at ground level? Begin by factoring x to create a constant term.

plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , plus or minus 3

0 , plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , 3

plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7

0 , plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7

What are the roots of the polynomial equation x cubed minus 6 x is equal to 3 x squared minus 8 ? Use a graphing calculator and a system of equations.

negative 40 , negative 4 , 5

negative 2 , 1 , 4

negative 4 , negative 1 , 2

negative 5 , 4 , 40

Which expression is equivalent to the fraction with numerator 15 A to the 8th power b to the 4th power and denominator 5 A to the 4th power b ?

3 A squared b to the 4th power

10 A to the 4th power b to the 4th power

10 A to the 4th power b cubed

3 A to the 4th power b cubed

Which fraction represents the decimal 0 point 8 8 8 8 dot dot dot ?

the fraction with numerator 1 comma 111 and denominator 1 comma 250

80 over 99

9 eighths

8 ninths

What is the cube root of negative 729 A to the 9th power b to the 6th power ?

negative 9 A cubed b squared

negative 9 A squared b cubed

negative 8 A cubed b squared

negative 8 A squared b cubed

Which expression is a difference of cubes?

x to the 8th power minus 6

x to the 6th power minus 6

x to the 6th power minus 8

x to the 8th power minus 8

What are the roots of the polynomial equation x to the 4th power plus x cubed is equal to 4 x squared plus 4 x ? Use a graphing calculator and a system of equations.

negative 1 , 0

0 , 1

negative 2 , negative 1 , 0 , 2

negative 2 , 0 , 1 , 2

Which second degree polynomial function has a leading coefficient of 2 and roots negative 3 and 5 ?

f of x is equal to 2 x squared plus 4 x minus 30

f of x is equal to 2 x squared minus 4 x minus 30

f of x is equal to 2 x squared minus 2 x minus 15

f of x is equal to 2 x squared plus 2 x minus 15

Which geometric series diverges?

the sum from n is equal to 1 to infinity of 2 thirds

negative 10 plus 4 minus 8 fifths plus 16 over 25 minus dot dot dot

3 fifths plus 3 tenths plus 3 over 20 plus 3 over 40 plus dot dot dot

the sum from n is equal to 1 to infinity of negative 12

Which expression is equivalent to c d to the 5th power ?

c to the 5th power plus d to the 5th power

c to the 5th power d to the 5th power

the fraction with numerator c to the 5th power and denominator d to the 5th power

c to the 5th power minus d to the 5th power

A polynomial function has a root of negative 6 with multiplicity 3 and a root of 2 with multiplicity 4 If the function has a negative leading coefficient and is of odd degree, which could be the graph of the function?

Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It starts from quadrant 2, passes through (negative 8 comma 8), crosses the x axis at (negative 6 comma 0), moves down and curves up at (negative 3 point 5 comma negative 3), and crosses the y axis at (0 comma negative 1). It then touches the x axis at (2 comma 0) and moves to quadrant 4 passing through (6 comma negative 8).

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 8 to 8 with an increment of 1. The curve begins at point arrow near "negative 7 comma negative 8" and extends upward from the lower-left quadrant. It rises sharply, crossing the x-axis at "negative 6 comma 0", and reaches a local maximum near "negative 3 point 5 comma 6". From there, it moves downward through the second quadrant, crossing the y-axis at "0 comma 2", and enters the first quadrant. It reaches a local minimum tangent to the x-axis at "2 comma 0", and then curves steeply upwards, terminating with an upward-pointing arrow near "5 comma 8".

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 8 to 8 with an increment of 1. The curve begins in the third quadrant near "negative 8 comma negative 1 point 5" with a downward-pointing arrow. Moving right, it rises into the second quadrant to a local maximum tangent to the x-axis at "negative 6 comma 0". It then decreases gradually to a local minimum in the third quadrant near "negative 1 comma negative 3". From there, it curves upward, crossing the y-axis at "0 comma negative 2 point 8", passing through the x-axis at "2 comma 0, and rising steeply into the first quadrant, where it terminates with an upward-pointing arrow near "4 comma 8".

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 8 to 8 with an increment of 1. The enters from the upper-left quadrant near "negative 8 comma 1" with an arrowhead pointing upward and to the left. It drops slightly to a local minimum tangent to the x-axis at "negative 6 comma 0", then rises gradually through the second quadrant, crossing the y-axis at a local maximum near "0 comma 1 point 5". From there, it enters the first quadrant, crossing the x-axis at " 2 comma 0", and curves steeply downward into the fourth quadrant where it terminates with a downward-pointing arrowhead near "5 comma negative 8".

What is the ninth term in the binomial expansion of open paren x minus 2 y close paren to the 13th power ?

329 comma 472 x to the 5th power y to the 8th power

negative 41 comma 184 x to the 8th power y to the 5th power

41 comma 184 x to the 8th power y to the 5th power

negative 329 comma 472 x to the 5th power y to the 8th power

What are the coefficients for the binomial expansion of open paren A plus b close paren cubed ?

1 , 4 , 6 , 4 , 1

1 , 2 , 1

1 , 1

1 , 3 , 3 , 1

What are the solutions of the equation x to the 4th power minus 5 x squared minus 36 is equal to 0 ? Use factoring to solve.

x is equal to plus or minus 2 i and x is equal to plus or minus 3

x is equal to plus or minus 2 and x is equal to plus or minus 3

x is equal to plus or minus 2 i and x is equal to plus or minus 3 i

x is equal to plus or minus 2 and x is equal to plus or minus 3 i

Which second degree polynomial function f of x has a leading coefficient of 3 and roots 4 and 1 ?

f of x is equal to 3 x squared minus 15 x plus 12

f of x is equal to 3 x squared plus 5 x plus 4

f of x is equal to 3 x squared plus 15 x plus 12

f of x is equal to 3 x squared minus 5 x plus 4

Which statement best describes the equation x to the 5th power plus x cubed minus 14 is equal to 0 ?

The equation is quadratic in form because it is a fifth-degree polynomial.

The equation is quadratic in form because the difference of the exponent of the lead term and the exponent of the middle term is 2 .

The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.

The equation is not quadratic in form because the exponent of the lead term is not the square of the exponent of the middle term.

What is the remainder when open paren 3 x cubed minus 2 x squared plus 4 x minus 3 close paren is divided by open paren x squared plus 3 x plus 3 close paren ?

3 x minus 11

28 x plus 30

28 x minus 36

What is the quotient of open paren 2 x to the 4th power minus 3 x cubed minus 3 x squared plus 7 x minus 3 close paren divided by open paren x squared minus 2 x plus 1 close paren ?

2 x squared plus x minus 3

2 x squared minus x

2 x squared plus x minus 3 minus the fraction with numerator 6 and denominator x squared minus 2 x plus 1

2 x to the 4th power minus 3 x cubed minus 11 halves

According to the Rational Root Theorem, the following are potential roots of f of x is equal to 6 x to the 4th power plus 5 x cubed minus 33 x squared minus 12 x plus 20 negative 5 halves , negative 2 , 1 , 10 thirds Which is an actual root of f of x ?

10 thirds

negative 2

negative 5 halves

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