Chapter Review on Polynomial Algebra
Chapter
Chapter 3
Section
Chapter Review on Polynomial Algebra
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Solutions 56 Videos

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

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Q3b

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

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Q4a

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

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Q4b

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

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Q4c

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

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Q4d

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

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Q5a

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

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Q5b

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

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Q5c

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

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Q5d

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

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Q6

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

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Q7

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

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

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Q8a

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

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Q8b

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

y = x^2 - 8x + 16

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Q8c

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})

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Q8d

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

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

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Q8e

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
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Q9a

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

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Q9a

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

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Q9b

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

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Q9c

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

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Q9d

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

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Q9e

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

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Q9f

Calculate each of the following using long division.

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

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Q10a

Calculate each of the following using long division.

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

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Q10b

Calculate each of the following using long division.

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

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Q10c

Calculate each of the following using long division.

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

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Q10d

Divide each polynomial by x + 2 using synthetic division.

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

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Q11a

Divide each polynomial by x + 2 using synthetic division.

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

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Q11b

Divide each polynomial by x + 2 using synthetic division.

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

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Q11c

Divide each polynomial by x + 2 using synthetic division.

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

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Q11d

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

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Q12a

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

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Q12b

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

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Q12c

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

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Q12d

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

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Q13

Factor the polynomial using the factor theorem.

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

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Q14a

Factor the polynomial using the factor theorem.

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

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Q14b

Factor the polynomial using the factor theorem.

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

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Q14c

Factor the polynomial using the factor theorem.

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

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Q14d

Factor fully.

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

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Q15a

Factor fully.

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

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Q15b

Factor fully.

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

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Q15c

Factor fully.

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

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Q15d

Factor the difference of cubes.

\displaystyle 64x^3 -27

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Q16a

Factor the difference of cubes.

\displaystyle 512x^3 - 125

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Q16b

Factor the difference of cubes.

\displaystyle 343x^3 -1728

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Q16c

Factor the difference of cubes.

\displaystyle 1331x^3 -1

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Q16d

Factor the sum of cubes.

\displaystyle 1000x^3 + 343

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Q17a

Factor the sum of cubes.

\displaystyle 1728x^3 + 125

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Q17b

Factor the sum of cubes.

\displaystyle 27x^3 + 1331

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Q17c

Factor the sum of cubes.

\displaystyle 216^3 + 2197

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Q17d

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.

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Q18