Chapter
Chapter 4
Section
Solutions 51 Videos

The model represents an algebraic expression. Identify the expression and its factors.

Q1a

The model represents an algebraic expression. Identify the expression and its factors.

Q1b

Factor

\displaystyle 20x^2 -4x 

Q2a

Factor

\displaystyle 3n^2 -6n + 15 

Q2b

Factor

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

Q2c

Factor

\displaystyle 6a(3- 7a) -5(3 - 7a) 

Q2d

The area of a rectangle is given by the relation \displaystyle A = 16x^2 -24 .

Determine the possible dimensions of this rectangle.

0.50mins
Q3

a) Write three polynomials whose terms have a greatest common factor of 4x^3 y.

b) Factor each polynomial you wrote in part a)

Q4

Identify each expression that is modelled below, and state its factors.

Q5a

Identify each expression that is modelled below, and state its factors.

Q5b

Factor fully

\displaystyle x^2 + 16x + 63 

Q6a

Factor fully

\displaystyle x^2 - 7x - 60 

Q6b

Factor fully

\displaystyle x^2 + 6x - 27 

Q6c

Factor fully

\displaystyle 5x^2 - 5x - 100 

Q6d

Examine the relation y = x^2+7x +12.

a) Write the relation in factored form.

b) Determine the coordinates of the x—intercepts.

c) Determine the coordinates of the vertex.

d) State the minimum value of the relation and where the minimum value occurs.

Q7

Identify the expression that is modelled below, and state its factors.

Q8a

Identify the expression that is modelled below, and state its factors.

Q8b

Factor fully.

\displaystyle 15x^2 -4x -4 

Q9a

Factor fully.

\displaystyle 20x^2+3x-2 

Q9b

Factor fully.

\displaystyle 7x^2-19x -6 

2.04mins
Q10a

Factor fully.

\displaystyle 5a^2+23a+15 

Q10b

Factor fully.

\displaystyle 12x^2-16x+5 

1.28mins
Q10c

Factor fully.

\displaystyle 6n^2 -11ny-10y^2 

1.59mins
Q10d

The profit on the watches they sell is determined by the relation P = -2n^2 + 120n -1000, where n is the number of watches sold and P is the profit in dollars.

a) What are the break-even points?

b) What is the maximum profit?

Q11

Identify the expression that is modelled below, and state its factors.

Q12a

Identify the expression that is modelled below, and state its factors.

0.52mins
Q12b

Factor fully.

\displaystyle 144x^2 -25 

Q13a

Factor fully.

\displaystyle 36a^2+12a + 1 

1.39mins
Q13b

Factor  \displaystyle 18x^5 - 512xy^2 

Q13c

Factor fully.

\displaystyle 4(x-2)^2-20(x -2) + 25 

Q13d

Factor fully.

\displaystyle (x + 5)^2-y^2 

0.43mins
Q13e

Factor fully.

\displaystyle x^2-6x+9-4y^2 

Q13f

Factor fully

\displaystyle 7x^2-26x -8 

Q16a

Factor fully

\displaystyle 64x^6 -25 

Q16b

Factor fully

\displaystyle 18ac - 12a - 15c + 10 

Q16c

Factor fully

\displaystyle 4x^2y - 44xy + 72y 

Q16d

Factor fully

\displaystyle 20x^2+61x + 45 

Q16e

Factor fully

\displaystyle z^4-13z^2+40 

Q16f

Factor fully

\displaystyle 2s^2+3s-5 

Q17a

Factor fully

\displaystyle 15-2x -x^2 

Q17b

Factor fully

\displaystyle x^4-4x^2-32 

Q17c

Factor fully

\displaystyle 16x^2-121y^2 

Q17d

Factor fully

\displaystyle 9 - 30a + 25a^2 

Q17e

Factor fully

\displaystyle x^2 + 16x + 64-25y^2 

Q17f

A box has dimension defined by V =18x^3 -2x + 45x^2 -5.

a) Determine expressions for the possible dimensions of these boxes.

b) Determine the dimensions and volume of a box if x = 2 cm

Q18

Determine the coordinates of the vertex of each relation.

\displaystyle y = x^2 -10x + 24 

Q19a

Determine the coordinates of the vertex of each relation.

\displaystyle y = 2x^2 -24x + 72 

Q19b

Determine the coordinates of the vertex of each relation.

\displaystyle y = -5x^2 + 500 

Q19c

Determine the coordinates of the vertex of each relation.

\displaystyle y = 2x^2-7x -4 

Q19d

Determine the coordinates of the vertex of each relation.

\displaystyle y = 4x^2 + 16x 

\displaystyle y = x^2 + 10x + 25