Chapter
Chapter 5
Section
Solutions 44 Videos

What binomial product does each diagram illustrate?

Q1a

What binomial product does each diagram illustrate?

Q1b

Simplify.

\displaystyle 4x^2(3x -5y + 8z) 

Q2a

Simplify.

\displaystyle 3m(6m^205m + 4) -(4m^3 - 8m^2 + 9) 

Q2b

Expand and simplify.

\displaystyle (y + 5)(y+ 9) 

Q3a

Expand and simplify.

\displaystyle (4x -7)(3x + 2) 

Q3b

Expand and simplify.

\displaystyle (6k + 1)(6k -1) 

Q3c

Expand and simplify.

\displaystyle (w -8)^2 

Q3d

Expand and simplify.

\displaystyle (4c + 5d)^2 

Q3e

Expand and simplify.

\displaystyle 2(x -4)(x - 7)-5(8x -9)(8x + 9) 

Q3f

The minimum stopping distance, after a delay of 1 s, for a particular car is modelled by the formula d = 0.006(s + 1)^2, , where d represents the stopping distance, in metres, and s represents the initial speed, in kilometres per hour.

a) Expand and simplify the formula.

b) Compare the results in both versions of the formula for an initial speed of 60 km/h.

Q4

Factor.

\displaystyle 9d^2e^2 +6d^3e 

Q5a

Factor.

\displaystyle 15p^2qr^3-25p^3q^2r + 5pqr 

Q5b

Factor.

\displaystyle 5(x + 6)-2(x + 6) 

Q5c

Factor.

\displaystyle 16x^2 + 8x -6x -3 

Q5d

a) Find an algebraic expression for the surface area of the square—based prism.

b) Expand and simplify your expression from part a).

c) Factor the resulting expression from part b).

Q6

Factor.

\displaystyle x^2 + 11x + 24 

Q7a

Factor.

\displaystyle y^2 -15y + 56 

Q7b

Factor.

\displaystyle n^2 - n - 90 

Q7c

Factor.

\displaystyle x^2 -14x + 49 

Q7d

Factor.

\displaystyle h^2 -100 

Q7e

Factor.

\displaystyle d^3 + 16d + 64 

Q7f

Factor fully.

\displaystyle 3k^2 + 12km -36 m^2 

Q8a

Factor fully.

\displaystyle 8y^2 + 19y + 6 

Q8b

Factor fully.

\displaystyle 9w^2-24w + 7 

Q8c

Factor fully.

\displaystyle 25a^2 + 60a + 36 

Q8d

Factor fully.

\displaystyle 121w^2 - 144 

Q8e

Factor fully.

\displaystyle 10x^2 -7xy - 6y^2 

Q8f

Explain how to determine whether or not you can factor 9x^2 - 10x + 18 over the integers.

Q9

The area of a rectangle is given as x^2 + 13x - 30.

a) Determine polynomials that represent the length and width of the rectangle.

b) What is the smallest integer value of x for which this area expression makes sense?

Q10

Determine all values of k so that each trinomial is a perfect square.

\displaystyle 36x^2 + kx + 121 

Q11a

Determine all values of k so that each trinomial is a perfect square.

\displaystyle 49k^2 -56d + k 

Q11b

Determine all values of k so that each trinomial is a perfect square.

\displaystyle 25x^2 -60xy + ky^2 

Q11c

Determine all values of k so that each trinomial is a perfect square.

\displaystyle ka^2 +30ab + 9b^2 

Q11d

a) Write an algebraic expression for the area of the shaded region.

b) Write the area expression in factored form.

c) Substitute x = 7 into both forms. Are the results the same? Why?

Q12

A parabola has equation \displaystyle y = 2(x + 6)^2 -2 

a) Expand and simplify to write the equation in the form y =ax^2 + bx + c.

b) Factor your equation from part a).

c) Do the three equations represent the same parabola? Justify your response.

Q13

The volume of a rectangular prism is given as 9x3 - 30x^2 + 25x.

a) Determine algebraic expressions for the dimensions.

b) Describe the faces of the prism.

Q14

Determine two values of k so that the trinomial can be factored as a difference of squares.

\displaystyle km^2 -25 

Q15a

Determine two values of k so that the trinomial can be factored as a difference of squares.

\displaystyle 16d^2 -k 

Q15b

Determine two values of k so that the trinomial can be factored as a difference of squares.

\displaystyle a^2 -kb^2 

Q15c

Factor to evaluate the difference.

\displaystyle 34^2-31^2 

Q16a

Factor to evaluate the difference.

\displaystyle 127^2-126^2 

Q16b

The first three diagrams in a pattern are shown.

a) Write a formula for the total number of small squares in the nth diagram.

b) Write a formula for the number of shaded small squares in the nth diagram.

c) Write a formula for the number of unshaded small squares in the nth diagram.

d) Write your formula from part c) in factored form.

e) Show that both forms of the formula give the same results for the 15th diagram.

a) Find all values of b so that x^2 + bx + 10 can be factored over the integers.
b) Find all values of b so that 4y^2 + by + 5 can be factored over the integers.