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(15-17) SOTS, sum and difference of cubes, systems

Total questions: 10

Worksheet time: 1hrs 10mins

Name
Class
Date
1.

Factor: x2+25x^2+25

a)

(x+5i)(x-5i)

b)

(x+5)(x-5)

c)

(x+25i)(x-25i)

d)

(x+5)(x+5)

2.

Factor: x2+81x^2+81

a)

(x+9i)(x-9i)

b)

(x+9)(x-9)

c)

(x+81i)(x-81i)

d)

(x+9)(x+9)

3.

Factor: x2+27x^2+27

a)

(x3i3)(x+3i3)\left(x-3i\sqrt[]{3}\right)\left(x+3i\sqrt[]{3}\right)

b)

(x3i2)(x+3i2)\left(x-3i\sqrt[]{2}\right)\left(x+3i\sqrt[]{2}\right)

c)

(xi27)(x+i27)\left(x-i\sqrt[]{27}\right)\left(x+i\sqrt[]{27}\right)

d)

(x9i3)(x+9i3)\left(x-9i\sqrt[]{3}\right)\left(x+9i\sqrt[]{3}\right)

4.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

5.

What are the solutions to the graphed system?

a)

(0,-2) and (3,1)

b)

(-2,0) and (2,0)

c)

(0,-2) and (3,1)

d)

(2,2) and (1,0)

6.
Find the solution(s).
a)
(-1,7) and (0,5)
b)
(-4,2) and (-5,8)
c)
(-2,6) and (10,15)
d)
(-2,4) and (6,12)
7.
Find the solution(s):
y = x2 - 4x + 6
y = x + 2
a)
(1, 4)
b)
(-1, 1) and (4, 2)
c)
(1, 3) and (4, 6)
d)
(1, 4) and (3, 6)
8.
Factor: 8x3 - 1
a)
(2x - 1)(4x2 + 2x + 1)
b)
(2x + 1)(4x2 - 2x + 1)
c)
(2x - 1)(4x2 - 2x - 1)
d)
(2x + 1)(4x2 +2x + 1)
9.
Factor
27x³-64
a)
(3x-4)(9x²+12x+16)
b)
(3x-4)(9x²-12x+16)
c)
(3x+4)(9x²-12x+16)
d)
(3x+4)(9x²+12x+16)
10.
Factor this difference of cubes:
x3 - 343
a)
(x + 7) (x2 - 7x + 49)
b)
(x2 + 1) (x - 343)
c)
(x - 7) (x2 + 7x + 49)
d)
(x2 - 343) (x + 1)