Mid Chapter Review
Chapter
Chapter 4
Section
Mid Chapter Review
Solutions 44 Videos

State the GCF for the following pair of terms.

24 and 60

Q1a

State the GCF for the following pair of terms.

x^3 and x^2

Q1b

State the GCF for the following pair of terms.

10y and 5y^2

Q1c

State the GCF for the following pair of terms.

-8a^2b and -12ab^2

Q1d

State the GCF for the following pair of terms.

c^4 d^2 and c^3 d

Q1e

State the GCF for the following pair of terms.

27 m^4 n^2 and 36 m^2 n^3

Q1f

Determine the missing factor.

7x - 28y = (\blacksquare)(x - 4y)

Q2a

Determine the missing factor.

6x - 9y = (3)(\blacksquare)

Q2b

Determine the missing factor.

24a^2 + 12b^2 = (\blacksquare)(2a^2 + b^2)

Q2c

Determine the missing factor.

x^2 - xy^3 = (x)(\blacksquare)

Q2d

Determine the missing factor.

-15x^2 + 6y^2 = (\blacksquare)(5x^2 -2y^2)

Q2e

Determine the missing factor.

a^4b^3 - a^3b^2 = (a^3b^2)(\blacksquare)

Q2f

The tiles in the model represent an algebraic expression. Identify the expression and the greatest common factor of its terms. Q3a

The tiles in the model represent an algebraic expression. Identify the expression and the greatest common factor of its terms. Q3b

Factor the expression.

7z + 35

Q4a

Factor the expression.

-28x^2 + 4x^3

Q4b

Factor the expression.

5m^2 - 10mn + 5

Q4c

Factor the expression.

x^2y^4 - xy^2 + x^3y

Q4d

A parabola is defined by the equation y = 5x^2 -15x. Explain how you would determine the coordinates of the vertex of the parabola, without using a table of values or graphing technology.

Q5

Factor the expression.

3x(5y - 2) + 5(5y - 2)

Q6a

Factor the expression.

4a(b + 6) - 3(b + 6)

Q6b

Factor the expression.

6xt - 2xy - 3t + y

Q6c

Factor the expression.

4ab + 4ac - b^2 - bc

Q6d

The model represents a quadratic expression. Identify the expression and its factors. Q7a

The model represents a quadratic expression. Identify the expression and its factors. Q7b

Determine the value of each symbol.

x^2 + \blacklozenge x + 12 = (x + 3)(x + \blacksquare)

Q8a

Determine the value of each symbol.

x^2 + \blacksquare x + \blacklozenge = (x + 3)(x + 3)

Q8b

Determine the value of each symbol.

x^2 - 12x + \blacksquare = (x - \blacklozenge)(x - \blacklozenge)

Q8c

Determine the value of each symbol.

x^2 - 7x + \blacklozenge = (x - 3)(x - \blacksquare)

Q8d

Factor.

x^2 + 8x - 33

Q9a

Factor.

n^2 + 7n -18

Q9b

Factor.

b^2 - 10b - 11

Q9c

Factor.

x^2 - 14x + 45

Q9d

Factor.

c^2 + 5c - 14

Q9e

Factor.

y^2 - 17y + 72

Q9f

Factor.

3a^2 - 3a - 36

Q10a

Factor.

x^3 - 6x^2 - 16x

Q10b

Factor.

2x^2 + 14x - 120

Q10c

Factor.

4b^2 - 36b + 72

Q10d

Factor.

-d^3 + d^2 + 30d

Q10e

Factor.

xy^3 + 2xy^2 + xy

Q10f

Deanna throws a rock from the top of a cliff into the air. The height of the rock above the base of the cliff is modeled by the equation h = -5t^2 + 10t + 75, where h is the height of the rock in metres and t is the time in seconds.

a) How high is the cliff?

b) When does the rock reach its maximum height?

c) What is the rock's maximum height?

Q11

When factoring a quadratic expression of the form x^2 + bx + c, why does it make more sense to consider the value of c before the value of b? Explain.

Use the quadratic relation determined by y = x^2 + 4x - 21.