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What is the completely factored form of 12 x y minus 9 x minus 8 y plus 6 ?

3 x open paren 4 y minus 3 close paren minus 2 times open paren 4 y plus 3 close paren

negative 6 x open paren 4 y minus 3 close paren open paren 4 y minus 3 close paren

open paren 3 x minus 2 close paren times open paren 4 y minus 3 close paren times open paren 4 y minus 3 close paren

open paren 3 x minus 2 close paren times open paren 4 y minus 3 close paren

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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?

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

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

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

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

Which statement describes the graph of this polynomial function? f of x is equal to x to the 4th power plus x cubed minus 2 x squared

The graph touches the x -axis at x is equal to negative 2 and x is equal to 1 and crosses the x -axis at x is equal to 0 .

The graph crosses the x -axis at x is equal to 2 and x is equal to negative 1 and touches the x -axis at x is equal to 0 .

The graph touches the x -axis at x is equal to 2 and x is equal to negative 1 and crosses the x -axis at x is equal to 0 .

The graph crosses the x -axis at x is equal to negative 2 and x is equal to 1 and touches the x -axis at x is equal to 0 .

What is the end behavior of the graph of the polynomial function f of x is equal to negative x to the 5th power plus 9 x to the 4th power minus 18 x cubed ?

As x rightarrow negative infinity , y rightarrow infinity and as x rightarrow infinity , y rightarrow infinity .

As x rightarrow negative infinity , y rightarrow negative infinity and as x rightarrow infinity , y rightarrow negative infinity .

As x rightarrow negative infinity , y rightarrow negative infinity and as x rightarrow infinity , y rightarrow infinity .

As x rightarrow negative infinity , y rightarrow infinity and as x rightarrow infinity , y rightarrow negative infinity .

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 ?

28 x plus 30

28 x minus 36

3 x minus 11

What is the completely factored form of 6 x squared minus 13 x minus 5 ?

open paren 2 x plus 5 close paren times open paren 3 x minus 1 close paren

open paren 2 x plus 1 close paren times open paren 3 x plus 5 close paren

open paren 2 x minus 5 close paren times open paren 3 x plus 1 close paren

open paren 2 x minus 1 close paren times open paren 3 x minus 5 close paren

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

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

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

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

What is the polynomial 3 y squared plus open paren y plus 7 close paren squared minus 15 after it has been fully simplified and written in standard form?

4 y squared plus 34

4 y squared plus 14 y plus 34

3 y squared plus y plus 34

4 y to the 4th power plus 34

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 minus 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 plus 5 x plus 4

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

The price that a company charged for a computer accessory is given by the equation 100 minus 10 x squared where x is the number of accessories that are produced, in millions. It costs the company 10 dollars to make each accessory. The company currently produces 2 million accessories and makes a profit of 100 million dollars. What other number of accessories produced yields the same profit?

1 point 4 5 million

48 million

40 million

3 point 4 5 million

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

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

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

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 .

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 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 plus 2 x minus 15

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

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 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".

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 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).

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 5 halves

negative 2

If 5 plus 6 i is a root of the polynomial function f of x , which of the following must also be a root of f of x ?

6 minus 5 i

6 plus 5 i

negative 5 minus 6 i

5 minus 6 i

The polynomial 8 x squared minus 8 x plus 2 minus 5 plus x is simplified to 8 x squared minus g x minus h What are the value of g and h ?

g is equal to negative 7 and h is equal to 7

g is equal to 9 and h is equal to negative 3

g is equal to 7 and h is equal to 3

g is equal to negative 9 and h is equal to 7

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