State the possible degree of each function, the sign of the leading coefficient, and the number of turning points.

For the following, write the equations of three cubic functions that have the given zeros and belong to the same family of functions.

-3, 6, 4

For the following, write the equations of three cubic functions that have the given zeros and belong to the same family of functions.

5, -1, -2

For the following, write the equations of three cubic functions that have the given zeros and belong to the same family of functions.

0, -1, 9, 10

For the following, write the equations of three cubic functions that have the given zeros and belong to the same family of functions.

9, -5, -4

For the following, write the equations of three quartic functions that have the given zeros and belong to the same family of functions.

-6, 2, 5, 8

For the following, write the equations of three quartic functions that have the given zeros and belong to the same family of functions.

4,-8, 1, 2

For the following, write the equations of three quartic functions that have the given zeros and belong to the same family of functions.

-7, 2, 3

For the following, write the equations of three quartic functions that have the given zeros and belong to the same family of functions.

-3, 3, -6, 6

Sketch the graph of f(x)=5 (x - 3) (x + 2) (x + 5) using the zeros and end behaviours.

Determine the equation of the function with zeros at \pm 1 and -2, and a y-intercept of -6. Then sketch the function.

Describe the transformations that were applied to y = x^2 to obtain each of the following functions.

y = -2(x -1)^2 + 23

Describe the transformations that were applied to y = x^2 to obtain each of the following functions.

y = (\frac{12}{13}(x + 9))^2 - 14

Describe the transformations that were applied to y = x^2 to obtain each of the following functions.

y = x^2 - 8x + 16

Describe the transformations that were applied to y = x^2 to obtain each of the following functions.

y =(x + \frac{3}{8})(x + \frac{3}{7})

Describe the transformations that were applied to y = x^2 to obtain each of the following functions.

y =40(-7(x - 10))^2 + 9

The function y = x^3 has undergone each of the following sets of transformations. List three points on the resulting function.

• vertically stretched by a factor of 25, horizontally compressed by a factor of 5, 6 horizontally translated 3 units to the right

The function y = x^3 has undergone each of the following sets of transformations. List three points on the resulting function.

The function y = x^3 has undergone each of the following sets of transformations. List three points on the resulting function.

reflected in the y-axis, horizontally stretched by a factor of 7, vertically translated 19 units down

The function y = x^3 has undergone each of the following sets of transformations. List three points on the resulting function.

reflected in the x-axis, vertically compressed by a factor of \frac{6}{11} , horizontally translated 11 5 units to the left, vertically translated 16 units up

The function y = x^3 has undergone each of the following sets of transformations. List three points on the resulting function.

vertically stretched by a factor of 100, horizontally stretched by a factor of 2, vertically translated 14 units up

The function y = x^3 has undergone each of the following sets of transformations. List three points on the resulting function.

eflected in the y-axis, vertically translated 45 units down

The function y = x^3 has undergone each of the following sets of transformations. List three points on the resulting function

reflected in the x-axis, horizontally compressed by a factor of \frac{7}{10} , horizontally translated 12 units to the right, vertically translated 6 units up

Calculate each of the following using long division.

\displaystyle (2x^3 + 5x^2 + 3x - 4) \div (x + 5)

Calculate each of the following using long division.

\displaystyle (x^4 + 4x^3 - 3x^2 - 6x -7) \div (x^2 - 8)

Calculate each of the following using long division.

\displaystyle (2x^4 -2x^2 + 3x -16) \div (x^3 + 3x^2 + 3x -3)

Calculate each of the following using long division.

\displaystyle (x^5 -8x^3 - 7x - 6) \div (x^4 + 4x^3 +4x^2 -x -3)

Divide each polynomial by x + 2 using synthetic division.

\displaystyle 2x^3 + 5x^2 -x -5

Divide each polynomial by x + 2 using synthetic division.

\displaystyle 3x^3 + 13x^2 + 17x + 3

Divide each polynomial by x + 2 using synthetic division.

\displaystyle 2x^4 + 5x^2 - x- 5

Divide each polynomial by x + 2 using synthetic division.

\displaystyle 2x^3 + 4x^2 - 5x -4

The divisor was divided into another polynomial, resulting in the given quotient and remainder. Determine the dividend.

divisor: x -9, quotient: 2x^2 + 11x -8, remainder : 3

The divisor was divided into another polynomial, resulting in the given quotient and remainder. Determine the dividend.

divisor: 4x +3, quotient: x^3 -2x + 7, remainder : -4

The divisor was divided into another polynomial, resulting in the given quotient and remainder. Determine the dividend.

divisor: 3x -4, quotient: x^3 + 6x^2 -6x -7, remainder : 3x^2 + x - 5

The divisor was divided into another polynomial, resulting in the given quotient and remainder. Determine the dividend.

divisor: 3x^2 + x - 5, quotient: x^4 -4x^3 + 9x -3, remainder : 2x -1

Without dividing, determine the remainder when x^3 + 2x^2 - 6x + 1 is divided by x + 2.

Factor the polynomial using the factor theorem.

\displaystyle x^3 -5x^2 -22x -16

Factor the polynomial using the factor theorem.

\displaystyle 2x^3 + x^2 -27x -36

Factor the polynomial using the factor theorem.

\displaystyle 3x^4 - 19x^3 + 38x^2 -24x

Factor the polynomial using the factor theorem.

\displaystyle x^4 + 11x^3 + 36x^2 + 16x -64

Factor fully.

\displaystyle 8x^3 -10x^2 -17x + 10

Factor fully.

\displaystyle 2x^3 + 7x^2 -7x -30

Factor fully.

\displaystyle x^4 -7x^3 + 9x^2 + 27x -54

Factor fully.

\displaystyle 4x^4 + 4x^3 - 35x^2 -36x -9

Factor the difference of cubes.

\displaystyle 64x^3 -27

Factor the difference of cubes.

\displaystyle 512x^3 - 125

Factor the difference of cubes.

\displaystyle 343x^3 -1728

Factor the difference of cubes.

\displaystyle 1331x^3 -1

Factor the sum of cubes.

\displaystyle 1000x^3 + 343

Factor the sum of cubes.

\displaystyle 1728x^3 + 125

Factor the sum of cubes.

\displaystyle 27x^3 + 1331

Factor the sum of cubes.

\displaystyle 216^3 + 2197

a) Factor the expression x^6 - y^6 completely by treating it as a difference of squares.

b) Factor the same expression by treating it as a difference of cubes.

c) Explain any similarities or differences in your final results.