Polynomial Chapter Review
Chapter
Chapter 2
Section
Polynomial Chapter Review
Solutions 32 Videos

i) Use the remainder theorem to determine the remainder for each division.

ii) Perform each division. Express the result in quotient form. Identify any restrictions on the variable.

\displaystyle x^3+9x^2 -5x + 3  divided by x - 2

Q1a

i) Use the remainder theorem to determine the remainder for each division.

ii) Perform each division. Express the result in quotient form. Identify any restrictions on the variable.

\displaystyle 12x^3-2x^2+ x -11  divided by 3x + 1

Q1b

i) Use the remainder theorem to determine the remainder for each division.

ii) Perform each division. Express the result in quotient form. Identify any restrictions on the variable.

\displaystyle -x^4-4x + 10x^3-x^2 + 15  divided by 2x- 1

Q1c

Determine the value of k such that when if f(x)=x^4+kx^3 -3x-5 is divided by x - 3, the remainder is -10.

Q2a

Determine the value of k such that when if f(x)=x^4 - kx^3 -3x-5 is divided by x + 3.

Q2b

For what value of b will the polynomial ,P(x) = 4x^3 - 3x^2 + bx + 6 have the same remainder when it is divided by x - 1 and by x+ 3?

Q3

Factor the polynomial fully.

\displaystyle x^3 -4x^2 + x + 6 

Q4a

Factor the polynomial fully.

\displaystyle 3x^3 -5x^2 - 26x - 8 

Q4b

Factor the polynomial fully.

\displaystyle 5x^4+12x^-101x^2+48x + 36 

Q4c

Rectangular blocks of limestone are to be cut up and used to build the front entrance of a new hotel. The volume, V, in cubic metres, of each block can be modelled by the function V(x) = 2x^3 + 7x^2 + 2x - 3.

a) Determine the dimensions of the blocks in terms of x.

b) What are the possible dimensions of the blocks when x =1?

Q6

Determine the value of k so that x + 3 is a factor of x^3+4x^2-2kx + 3.

Q7

Determine the real roots of the question.

\displaystyle (5x^2 + 20)(3x^2 -48) = 0 

Q9a

Determine the real roots of the question.

\displaystyle (2x^2-x-13)(x^2 + 1) = 0 

Q9b

\displaystyle 7x^3 + 5x^2 -5 -3 = 0 

Q10a

\displaystyle -x^3 + 9x^2 = x + 6 

You may use a graphing device for this question

Q10b

The specifications for a cardboard box state that the width is 5 cm less than the length, and the height is 1 cm more than double the length. Write an equation for the volume of the box and find possible dimensions for a volume of 550 cm^3.

You may use a graphing device for this question

Q11

Examine the following functions. Which function does not belong to the same family? Explain.

A \displaystyle y = 3.5(x + 2)(x-1)(x-3) 

B \displaystyle y = -0/2(x - 3)(2x+4)(2x-3) 

C \displaystyle y = (4x -12)(x + 2)(x - 1) 

D \displaystyle y = -7(x -1)(x - 3)(x + 2) 

Q12

a) Determine an equation, in simplified form, for the family of cubic functions with zeros 2 \pm \sqrt{5} and 0.

b) Determine an equation for the member of the family with graph passing through the point (2, 20).

Q13

Determine an equation for the function represented by this graph. Q14

Solve using using technology.

\displaystyle x^2 +3x - 5 \geq 0 

You may use a graphing device for this question

Q15a

Solve using using technology.

\displaystyle 2x^3 -13x^2 +17x + 12 > 0 

You may use a graphing device for this question

Q15b

Solve using using technology.

\displaystyle x^3 -2x^2 -5x + 2 < 0 

Q15c

Solve using using technology.

\displaystyle 3x^3 + 4x^2 -35x -12 \leq 0 

You may use a graphing device for this question

Q15d

Solve using using technology.

\displaystyle -x^4 -2x^3 + 4x^2 + 10x + 5 < 0 

You may use a graphing device for this question

Q15e

A section of a water tube ride at an amusement park can be modelled by the function

h(t) = -0.002t^4 + 0.104t^3 -1.69t^2 + 8.5t + 9,

where t is the time, in seconds, and h is the height, in metres, above the ground. When will the riders be more than 15 m above the ground?

You may use a graphing device for this question

Q16

Solve the inequality. Show your solution on a number line.

\displaystyle (5x + 4)(x - 4)< 0 

Q17a

Solve the inequality. Show your solution on a number line.

\displaystyle -(2x + 3)(x - 1)(3x -2) \leq 0 

Q17b

Solve the inequality. Show your solution on a number line.

\displaystyle (x^2 + 4 + 4)(x^2- 25)> 0 

Q17c

Solve by factoring.

\displaystyle 12x^2 + 25x - 7\geq 0 

Q18a

Solve by factoring.

\displaystyle 6x^3 + 13x^2 -41x + 12 \leq 0 

\displaystyle -3x^4 + 10x^3 + 20x^2 -40x + 32 < 0