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

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

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

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

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

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

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

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

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

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

Q5d

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

Q6

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

Q7

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

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

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

Q8b

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

y = x^2 - 8x + 16

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}) 

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 

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
Q9a

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

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

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

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

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

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

Q9f

Calculate each of the following using long division.

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

Q10a

Calculate each of the following using long division.

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

Q10b

Calculate each of the following using long division.

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

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) 

Q10d

Divide each polynomial by x + 2 using synthetic division.

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

Q11a

Divide each polynomial by x + 2 using synthetic division.

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

Q11b

Divide each polynomial by x + 2 using synthetic division.

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

Q11c

Divide each polynomial by x + 2 using synthetic division.

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

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

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

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

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

Q12d

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

Q13

Factor the polynomial using the factor theorem.

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

Q14a

Factor the polynomial using the factor theorem.

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

Q14b

Factor the polynomial using the factor theorem.

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

Q14c

Factor the polynomial using the factor theorem.

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

Q14d

Factor fully.

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

Q15a

Factor fully.

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

Q15b

Factor fully.

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

Q15c

Factor fully.

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

Q15d

Factor the difference of cubes.

\displaystyle 64x^3 -27 

Q16a

Factor the difference of cubes.

\displaystyle 512x^3 - 125 

Q16b

Factor the difference of cubes.

\displaystyle 343x^3 -1728 

Q16c

Factor the difference of cubes.

\displaystyle 1331x^3 -1 

Q16d

Factor the sum of cubes.

\displaystyle 1000x^3 + 343 

Q17a

Factor the sum of cubes.

\displaystyle 1728x^3 + 125 

Q17b

Factor the sum of cubes.

\displaystyle 27x^3 + 1331 

Q17c

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.