2.6 Solve Factorable Polynomial Inequalities
Chapter
Chapter 2
Section
2.6
Lectures 8 Videos

Ex1 and Interval Notation  1.55mins
Ex1 and Interval Notation

Double Inequality example 1.44mins
Double Inequality example 2.06mins
Solutions 39 Videos

Solve each inequality. Show each solution on a number line.

x + 3 \leq 5

0.18mins
Q1a

Solve each inequality. Show each solution on a number line.

 \displaystyle 2x + 1 \leq -4 

0.30mins
Q1b

Solve each inequality. Show each solution on a number line.

 \displaystyle 5 - 3x \geq 6 

0.28mins
Q1c

Solve each inequality. Show each solution on a number line.

 \displaystyle 7x < 4 + 3x 

0.31mins
Q1d

Solve each inequality. Show each solution on a number line.

 \displaystyle 2 - 4x > 5x + 20 

0.27mins
Q1e

Solve each inequality. Show each solution on a number line.

 \displaystyle 2(1 - x) \leq x -8 

0.39mins
Q1f

Solve by considering all cases. Show each solution on a number line.

(x + 2)(x - 4) > 0

2.14mins
Q2a

Solve by considering all cases. Show each solution on a number line.

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

1.51mins
Q2b

Solve using intervals. Show each solutions on a number line.

(x +3)(x - 2) > 0

1.09mins
Q3a

Solve using intervals. Show each solutions on a number line.

(x - 6)(x -9) \leq 0

0.44mins
Q3b

Solve using intervals. Show each solutions on a number line.

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

1.10mins
Q3c

Solve.

(x + 2)(3 -x)(x + 1) < 0

1.04mins
Q4a

Solve.

(-x + 1)(3x - 1)(x + 7) \geq 0

1.03mins
Q4b

Solve.

(7x + 2)(1 -x)(2x + 5) > 0

1.03mins
Q4c

Solve.

(x + 4)(-3x + 1)(x + 2) \leq 0

0.57mins
Q4d

Solve by considering all cases. Show each solutions on a number line.

x^2 - 8x + 15 \geq 0

1.48mins
Q5a

Solve.

x^2 - 2x -15 < 0

0.39mins
Q5b

Solve.

15 x^2 - 14x - 8 \leq 0

0.57mins
Q5c

Solve by considering all cases. Show each solutions on a number line.

x^3 - 2x^2 - 5x + 6 < 0

4.56mins
Q5d

Solve by considering all cases. Show each solutions on a number line.

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

1.20mins
Q5e

Solve using intervals.

x^3 + 6x^2 + 7x + 12 \geq 0

0.21mins
Q6a

Solve using intervals.

x^3 + 9x^2 + 26x + 24 < 0

2.42mins
Q6b

Solve using intervals.

5x^3 - 12x^2 -11x + 6 \leq 0

1.42mins
Q6c

Solve using intervals.

6x^4 - 7x^3 -4x^2 + 8x + 12 > 0

0.17mins
Q6d

Solve.

x^2 + 4x - 5 \leq 0

0.26mins
Q7a

Solve.

-2x^3 + x^2 + 13x + 6 < 0

2.12mins
Q7b

Solve. You may use a graphing device.

2x^3 + x^2 - 2x - 1 > 0

1.27mins
Q7c

Solve.

x^3 -5x + 4 \geq 0

1.27mins
Q7d

Chocolates are packaged in boxes that measure 18 cm by 20 cm by 6 cm. A larger box is being designed by increasing the length, width, and height of the smaller box by the same length so that the volume is at least 5280 cm^3. What are the minimum dimensions of the large box?

Q8

The price, p, in dollars, of a stock t years after 1999 can be modelled by the function p(t) = 0.5t^3-5.5t^2 + 14t. When will the price of the stock be more than \\$90?

1.30mins
Q9

Solve the inequality x^3 - 5x^2 + 2x + 8 < 0 by

2.31mins
Q10

Solve (x + 4)(x - 2)(x+1)(x -1) \leq 0.

1.19mins
Q11

Solve x^5+7x^3 + 6x < 5x^4 + 7x^2 + 2. You may use a graphing device for this.

2.58mins
Q12

A demographer develops a model for the population, P, of a small town years from today such that P(n) = -0.15n^5 + 3n^4 + 5560.

When will the population of the town be between 10 242 and 25325?

3.52mins
Q13a

A demographer develops a model for the population, P, of a small town years from today such that P(n) = -0.15n^5 + 3n^4 + 5560.

When will the population of the town be more than 30 443?

1.16mins
Q13b

A demographer develops a model for the population, P, of a small town years from today such that P(n) = -0.15n^5 + 3n^4 + 5560.

Will the model be valid after 20 years? Explain.

0.34mins
Q13c

Write two possible quartic inequalities, one using the less than or equal to symbol and the other using the greater than or equal symbol, that correspond to the following solution:

• -6 - \sqrt{2} < x < -6 + \sqrt{2} or
• 6 - \sqrt{2} < x < 6 + \sqrt{2}
2.05mins
Q14

Determine the exact length of PQ in the figure. Determine an equation for the line that is tangent to the circle with equation x^2 + y^2 - 25 = 0 and passes through the point (4, 3).