4.3 Solving Polynomial Inequalities
Chapter
Chapter 4
Section
4.3
Solutions 38 Videos

Solve each of the following using a number line strategy. Express your answers using set notation.

(x+2)(x-3)(x+1) \geq 0

1.58mins
Q1a

Solve each of the following using a number line strategy. Express your answers using set notation.

-2(x-2)(x-4)(x+3) < 0

1.16mins
Q1b

Solve each of the following using a number line strategy. Express your answers using set notation.

(x-3)(5x+2)(4x-3) < 0

1.11mins
Q1c

Solve each of the following using a number line strategy. Express your answers using set notation.

(x-5)(5x+2)(4x-3) < 0

1.11mins
Q1d

For each graph shown, determine where f(x) \leq 0 Express your answers using interval notation. 0.33mins
Q2a

For each graph shown, determine where f(x) \leq 0 Express your answers using interval notation. 0.15mins
Q2b

For each graph shown, determine where f(x) \leq 0 Express your answers using interval notation. 0.22mins
Q2c

For each graph shown, determine where f(x) \leq 0 Express your answers using interval notation. 0.18mins
Q2d

If f(x)=2x^3-x^2+3x+10 and g(x)=x^3+3x^2+2x+4, determine when f(x) > g(x) using a factor table strategy.

2.21mins
Q3

Solve the inequality x^3-7x^2+4x+12 > x^2-4x-9 using a graphing calculator.

0.52mins
Q4

For each of the following polynomial functions, state the intervals where f(x) > 0. 0.24mins
Q5a

For each of the following polynomial functions, state the intervals where f(x) > 0. 0.22mins
Q5b

For each of the following polynomial functions, state the intervals where f(x) > 0. 0.27mins
Q5c

For each of the following polynomial functions, state the intervals where f(x) > 0. 0.26mins
Q5d

Solve the following inequalities.

(x-1)(x+1) > 0

0.18mins
Q6a

Solve the following inequalities.

(x+3)(x-4) < 0

0.20mins
Q6b

Solve the following inequalities.

(2x+1)(x-5) \geq 0

0.23mins
Q6c

Solve the following inequalities.

-2x(x+7)(x-2) < 0

0.40mins
Q6d

Solve the following inequalities.

(x-3)(x+1) + (x-3)(x+2) \geq 0

0.50mins
Q6e

Solve the following inequalities.

2x(x+4) - 3(x+4) \leq 0

0.26mins
Q6f

x^2-6x+9 \geq 16

0.47mins
Q7a

x^4-8x < 0

1.02mins
Q7b

x^3+4x^2+x \leq 6

1.21mins
Q7c

x^4-5x^2+4 > 0

0.58mins
Q7d

3x^3-3x^2-2x \leq 2x^3-x^2+x

0.48mins
Q7e

x^3-x^2-3x+3 > -x^3+2x+5

1.29mins
Q7f

For the following pair of functions, determine when f(x) < g(x). 0.38mins
Q8

Consider x^3+11x^2+18x+10 > 10.

What is the equation of the corresponding function that could be graphed and used to solve this inequality?

Explain how the graph of the corresponding function can be used in this case to solve the inequality.

Solve this inequality algebraically.

1.14mins
Q9

Determine an expression for f(x) in which f(x) is a quartic function, f(x) > 0 when -2 < x < 1, f(x) \leq 0 when x < -2 or x > 1, f(x) has a double root when x = 3, and f(-1) = 96.

1.56mins
Q10

The viscosity, v, of oil used in cars is related to its temperature, t, by the formula v = -t^3-6t^2+12t+50, where each unit of t is equivalent to 50^{\circ}C.

Graph the function.

Determine the temperature range for which v>0 to two decimal places.

Determine the temperature ranges for which 15 < v < 20 to two decimals places.

3.50mins
Q11

An open-topped box can be made from a sheet of aluminium measuring 50 cm by 30 cm by cutting congruent squares from the four corners and folding up the sides. Write a polynomial function to represent the volume of such a box. Determine the range of side lengths that are possible for each square that is cut out and removed that result in a volume greater than 4000 cm^{3}. 4.32mins
Q13

Without a calculator, explain why the inequality 2x^{24}+x^4+15x^2+80 < 0 has no solution.

1.13mins
Q14a

Without a calculator, explain why -4x^{12}-7x^6+9x^2+20 < 30 + 11x^2 has a solution of -\infty < x < \infty.

2.21mins
Q14b

Which one of the steps has an error?

Solve: (x+1)(x-2) > (x+1)(-x+6).

(Step 1) Divide both sides by x+1 and get x-2 > -x+6.

(Step 2) Add x to both sides: 2x-2 > 6.

(Step 3) Add 2 to both sides: 2x > 8.

(Step 4) Divide both sides by 2: x > 4.

1.01mins
Q15

Use what you know about the factoring method to solve the following inequalities.

 \displaystyle \frac{x^2+x-12}{x^2+5x+6} < 0 

1.15mins
Q17a

Use what you know about the factoring method to solve the following inequalities.

 \displaystyle \frac{x^2-25}{x^3+6x^2+5x} > 0 

2.15mins
Q17b

Solve the inequality (x+1)(x-2)(2^x) \geq 0 algebraically.

0.31mins
Q18
Lectures 4 Videos

ex x^2 - 3x + 2\leq 0. 2.06mins 1.58mins

## Polynomial Inequality ex1

ex Solve for x.

 (x - 1)^2(x + 2)^3(x+ 5) \leq 0  