Chapter Review of Polynomials
Chapter
Chapter 2
Section
Chapter Review of Polynomials
Solutions 49 Videos

Sketch models to represent each of the following algebraic expressions. The variables x and y are not equal.

\displaystyle y^2 

0.19mins
Q1a

Sketch models to represent each of the following algebraic expressions. The variables x and y are not equal.

\displaystyle y^3 

0.35mins
Q1b

Sketch models to represent each of the following algebraic expressions. The variables x and y are not equal.

\displaystyle 2x 

0.21mins
Q1c

Sketch models to represent each of the following algebraic expressions. The variables x and y are not equal.

\displaystyle (2x)^2 

0.16mins
Q1d

Rob is finishing a floor with square tiles. Each tile has an area of 412 cm^2. Estimate the length of the side of each tile.

0.24mins
Q2

Why do you get the same result for each of the following expressions? Show your work using Exponent Laws.

(a) \displaystyle \frac{5^7}{5^4}

(b) \displaystyle \frac{5^6}{5^3}

(c) \displaystyle\frac{(5^4)(5^5)}{5^6}

(d) \displaystyle\frac{(5^4)(5)}{(5)(5)}

0.35mins
Q3

Simplify, and then evaluate for x = -2 and y = 3

\displaystyle \frac{(x^3)(x^4)}{x^6} 

0.15mins
Q4a

Simplify, and then evaluate for x = -2 and y = 3

\displaystyle \frac{(y^6)(x^4)}{(x^2)(y^4)} 

0.28mins
Q4b

Simplify, and then evaluate for x = -2 and y = 3

\displaystyle \frac{-32x^6}{16x^3} 

0.26mins
Q4c

If you know that the product of two numbers is 9^6 and quotient is 9^2, which of the following could be the two numbers?

0.51mins
Q5

About how long does it take for light to travel from one end of our galaxy to the other?

• It is about 9.5 \times 10^6 km from one end of our galaxy to the other.
• Light travels at about 1.1 \times 10^9 km/h.
0.50mins
Q6

Simplify.

\displaystyle (a^3)^2 

0.11mins
Q7a

Simplify.

\displaystyle (4x^3)^4 

0.19mins
Q7b

Simplify.

\displaystyle \frac{(2^3y^4)^3}{(2^4y^3)^2} 

0.42mins
Q7c

Which of the following is equal to 0?

• a)(10^3)^5 -(10^5)^3
• b) (9^2)^2-(3^4)^2
0.34mins
Q8

Express each of the following as a power with a prime base.

8^3

0.22mins
Q9a

Express each of the following as a power with a prime base.

25^4

0.13mins
Q9b

Express each of the following as a power with a prime base.

9^3

0.13mins
Q9c

The length of the side of a cube is 5^3. Express its surface area (SA) and volume (V) using powers and simplify each expression.

0.45mins
Q10

Simplify.

\displaystyle 5y -4y 

0.09mins
Q11a

Simplify.

\displaystyle 3xy^2 + 3xy^2 

0.15mins
Q11b

Simplify.

\displaystyle 2x^2 - 5x + 5x^2 -x 

0.17mins
Q11c

Simplify.

\displaystyle y^2 + 5xy + y^2 - xy 

0.14mins
Q11d

Simplify.

\displaystyle \frac{4}{5}a - \frac{1}{5}a 

0.14mins
Q12a

Simplify.

\displaystyle 2\frac{1}{2}a + \frac{2}{3}b + \frac{1}{2}a-\frac{1}{3}b 

0.28mins
Q12b

Simplify.

\displaystyle -1.75m + 2.7 -2.25m + 2.3 

0.21mins
Q12c

Mindy and Kimberly have a picture framing business. Mindy cuts the wooden frames. She charges \$25 for each one plus \$10/h for her labour. Kimberly cuts the picture mats and assemblies the product. She assembles $8 for each mat plus \$ 9/h for her labour.

(a) Represent Mindy's bill as a polynomial.

(b) Represent Kimberly's bit las a polynomial.

(c) Write a new polynomial that represents their total charge to dream a picture. Assume that they both work h hours on the frame.

(d) Calculate the cost for a frame if they both work 5 h on it.

1.14mins
Q13

Expand. check one of your answer using a different tool or strategy.

3(y - 2)

0.12mins
Q14a

Expand. check one of your answer using a different tool or strategy.

x(2x+ 4)

0.14mins
Q14b

Expand. check one of your answer using a different tool or strategy.

5m(3m^3 + 2n)

0.29mins
Q14c

Expand. check one of your answer using a different tool or strategy.

-3x(x^2 -x)

0.26mins
Q14d

Expand. check one of your answer using a different tool or strategy.

2y^3(y^3 + 3y^2 - y)

0.30mins
Q14e

Expand. check one of your answer using a different tool or strategy.

-a^2(2a -5a^2+4a^3)

0.36mins
Q14f

Expand.

 \displaystyle \frac{1}{3}(3x +12)

0.16mins
Q15a

Expand.

\displaystyle \frac{2}{5}(\frac{5}{8}a +10b)

0.24mins
Q15b

Expand.

-1.5m(2.8m + 2.2)

0.29mins
Q15c

Rick runs a pet store and is building rectangular pens for the animals. The length of the pens is always 20 cm longer than the width.

(a) One way of determining the perimeter is to use P = 2(l + w). Use this formula to create an expression for the perimeter in terms of x.

(b) Simplify your formula in part (a).

0.26mins
Q16ab

Rick runs a pet store and is building rectangular pens for the animals. The length of the pens is always 20 cm longer than the width.

• Find the perimeter of a pen with a width of 45 cm.
0.22mins
Q16c

Expand and simplify. Check one of your answers using a different tool or strategy.

2(x - 3) + 3(x + 2)

0.16mins
Q17a

Expand and simplify. Check one of your answers using a different tool or strategy.

3(y^2 + y-2)-(y^2+2y+4)

0.37mins
Q17b

Expand and simplify. Check one of your answers using a different tool or strategy.

2x(3x - 2) + x^2 + 2(x^2+3)

0.33mins
Q17c

Expand and simplify. Check one of your answers using a different tool or strategy.

3x(4x^2-5x) + x^3 -x^2

0.27mins
Q17d

Ms. Smith needs fabric pieces for an art project for her students. The pieces will be cut to two rectangular sizes, as shown.

Determine a simplified expression for the area of fabric needed if 14 students choose the larger size and 12 choose the smaller size.

1.00mins
Q18a

Ms. Smith needs fabric pieces for an art project for her students. The pieces will be cut to two rectangular sizes, as shown.

The class decides that the width of each piece of fabric will be 20 cm. Use your answer from part a) to determine how much material will be needed.

0.40mins
Q18b

Expand and simplify.

\displaystyle \frac{1}{4}(8x - 12) -\frac{1}{2}(6 - 14x)

0.30mins
Q19a

Expand and simplify.

\displaystyle \frac{5}{6}(6x - 18y) +\frac{2}{3}(21x - 6y)

0.42mins
Q19b

Expand and simplify.

\displaystyle \frac{5}{6}(6x - 18y) +\frac{2}{3}(21x - 6y)

1.13mins
Q19c

Mike has a baseball card collection. He is wondering about the future value of his rookie and big star cards.

Write an expression that represents the combined value of these cards in y years.