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Lectures
4 Videos

*ex* x^2 - 3x + 2\leq 0.

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2.06mins

Quadratic Inequality ex1

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1.58mins

Quadratic Inequality ex2

*ex* Solve for x.

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

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1.30mins

Polynomial Inequality ex1

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1.46mins

Polynomial Inequality ex2

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`

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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`

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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`

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1.11mins

Q1c

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

`(x -5)(4x + 1)(2x -5) \geq 0`

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1.11mins

Q1d

For each graph shown, determine where `f(x) \leq 0`

Express your answers using interval notation.

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0.33mins

Q2a

For each graph shown, determine where `f(x) \leq 0`

Express your answers using interval notation.

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0.15mins

Q2b

For each graph shown, determine where `f(x) \leq 0`

Express your answers using interval notation.

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0.22mins

Q2c

For each graph shown, determine where `f(x) \leq 0`

Express your answers using interval notation.

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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.

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2.21mins

Q3

Solve the inequality `x^3-7x^2+4x+12 > x^2-4x-9`

using a graphing calculator.

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0.52mins

Q4

For each of the following polynomial functions, state the intervals where `f(x) > 0`

.

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0.24mins

Q5a

For each of the following polynomial functions, state the intervals where `f(x) > 0`

.

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0.22mins

Q5b

For each of the following polynomial functions, state the intervals where `f(x) > 0`

.

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0.27mins

Q5c

For each of the following polynomial functions, state the intervals where `f(x) > 0`

.

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0.26mins

Q5d

Solve the following inequalities.

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

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0.18mins

Q6a

Solve the following inequalities.

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

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0.20mins

Q6b

Solve the following inequalities.

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

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0.23mins

Q6c

Solve the following inequalities.

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

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0.40mins

Q6d

Solve the following inequalities.

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

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0.50mins

Q6e

Solve the following inequalities.

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

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0.26mins

Q6f

Solve the following inequalities algebraically. Confirm your answer with a graph.

`x^2-6x+9 \geq 16`

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0.47mins

Q7a

Solve the following inequalities algebraically. Confirm your answer with a graph.

`x^4-8x < 0`

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1.02mins

Q7b

Solve the following inequalities algebraically. Confirm your answer with a graph.

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

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1.21mins

Q7c

Solve the following inequalities algebraically. Confirm your answer with a graph.

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

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0.58mins

Q7d

Solve the following inequalities algebraically. Confirm your answer with a graph.

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

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0.48mins

Q7e

Solve the following inequalities algebraically. Confirm your answer with a graph.

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

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1.29mins

Q7f

For the following pair of functions, determine when `f(x) < g(x)`

.

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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.

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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`

.

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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.

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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}`

.

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4.32mins

Q13

Without a calculator, explain why the inequality `2x^{24}+x^4+15x^2+80 < 0`

has no solution.

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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`

.

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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`

.

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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
```

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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
```

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2.15mins

Q17b

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

algebraically.

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0.31mins

Q18