Question

Jeanie wrote the correct first step to divide 8z2 + 4z – 5 by 2z.



Which shows the next step?

4z + 2 –
4z2 + 2 –
4z2 + 2 –
4z + 2 –



Which expression shows the first step in dividing 5x + 3 by x?








Consider the division of 4h2 + 2h + 6 by 2h.







What are the values of A and B?

A = 2 and B = 1
A = 2h and B = 1
A = and B =
A = and B =



Fiona divided 3x2+5x-3 by 3x+2. The expression represents the remainder over the divisor.



What is the value of a?

-5
-1
1
5



What is the quotient?



4x2 + 15 +
4x + 15 +
4x2 + 15 +
4x + 15 +



Consider the division of 8y2 – 12y + 4 by 4y.





What are the values of a and b?

a = 2y and b = 3
a = and b = –3y
a = 2y and b = –3
a = and b = 3y



The area of the base of a cylinder is found by dividing the volume of the cylinder by its height.



If the volume of the cylinder is represented by 5x2 + 15x + 2 and the height is 5x, which expression represents the area of the base?

x2 + 3x +
5x (5x2 + 15x + 2)
x + 3 +
x (x2 + 3x +2)



The height of a rectangular prism is found by dividing volume, V, by the base area, B.





If the volume of the rectangular prism is represented by 6x2 – 2x + 8 and the base area is 2x – 4, which expression represents the height?

3x + 5 –
3x – 7 +
3x + 5 +
3x – 7 –



Aramis showed the division of 6p2 + 9p + 3 by 3p.

A + 3 + B

What are the values of A and B?

A = 2p and B = p
A = 3p and B = p
A = and B =
A = 2p and B =



Consider the division of 15h2 + 10h + 25 by 5h.





= X + Y +

What are the values of X and Y?

X = 3 and Y = 2
X = and Y =
X = 3h and Y = 2
X = and Y =

Answer 1

1) Next step for (8z^2 + 4z − 5) ÷ 2z:
Answer: 4z + 2 − … (so the quotient begins 4z + 2 and the remainder term is −5/(2z))

2) First step in dividing 5x + 3 by x:
Answer: 5 + 3/x

3) (4h^2 + 2h + 6) ÷ 2h — values of A and B (in A + B + remainder/divisor):
Answer: A = 2h, B = 1 (quotient = 2h + 1, remainder term = 3/h)

4) Fiona divided 3x^2 + 5x − 3 by 3x + 2. The remainder is −5, so:
a = −5

5) What is the quotient (for Fiona’s division)?
Answer: x + 1 (remainder −5 gives −5/(3x+2))

6) (8y^2 − 12y + 4) ÷ 4y — values of a and b:
Answer: a = 2y, b = −3 (quotient = 2y − 3, remainder term = 1/y)

7) Cylinder base area = (5x^2 + 15x + 2) ÷ 5x:
Answer: x + 3 + 2/(5x)

8) Height = (6x^2 − 2x + 8) ÷ (2x − 4):
Answer: 3x + 5 + 28/(2x − 4) (equivalently 3x + 5 + 14/(x − 2))

9) (6p^2 + 9p + 3) ÷ 3p written as A + 3 + B:
Answer: A = 2p, B = 1/p (quotient = 2p + 3, remainder term = 1/p)

10) (15h^2 + 10h + 25) ÷ 5h = X + Y + remainder/divisor:
Answer: X = 3h and Y = 2 (remainder term = 5/h)