Question

Complex Algebra! Please Help! I have been struggling really bad.

1. x4 – 3x2 + 2y – 1 is a polynomial of degree

A) 3
B) 2
C) 4
D) 5

2. For a given function ƒ(x), the translation ƒ(x – 2) + 3 means the function will shift

A) right 3 and upward 2.
B) left 3 and downward 2.
C) left 2 and downward –3.
D) right 2 and upward 3.

3. Which of the following describes the end behavior of the function ƒ(x) = x4 + 3x3 – 2x + 7?

A) As x → –∞, y → –∞ and as x → +∞, y → +∞
B) As x → –∞, y → –∞ and as x → +∞, y → –∞
C) As x → –∞, y → +∞ and as x → +∞, y → –∞
D) As x → –∞, y → +∞ and as x → +∞, y → +∞

4. Use Pascal's triangle to expand (x + 3)4.

A) x4 – 20x3 + 90x2 – 135x + 81

B) x4 – 12x3 + 54x2 – 108x + 81

C) x4 + 12x3 + 54x2 + 108x + 81

D) x4 + 20x3 + 90x2 + 135x + 81

5. Use Pascal's triangle to find the coefficient of the third term in the expansion of (a + b)2.

A) 2
B) 4
C) 1
D) 3

Answer 1

#1. The degree is the highest power of x -- x^4
#2. f(x-h)+k shifts right h, up k
#3. Since the highest term is +x^4, y is always positive for large x
#4. (x+3)^4 = x^4 + 4x^3*3 + 6x^2*3^2 + 4x*3^3 + 3^4
#5. (a+b)^2 = a^2 + 2ab + b^2