math 4th quarter LT review

1. 4TH QUARTER LONG TEST REVIEW

2. QUESTION 1
 Find the equation of the circle in general form with
center (-3, 2) and radius length 6.
x2 + y2 + 6x – 4y – 23 = 0

3. QUESTION 2
 Determine the center and the radius of the circle
x2 + y2 + 4y + 10x = -4.
C(-5, -2), r = 5

4. QUESTION 3
 Find the equation of a circle in standard form
tangent to the line x = 6 and with center at (2, -3).
(x - 2)2 + (y + 3)2 = 16

5. QUESTION 4
 What polynomial will have a quotient of 3x3 + 2x -1
when divided by x - 3.
3x4 – 9x3 + 2x2 – 7x + 3

6. QUESTION 5
 Find the remainder when -4x99 + 21x40 – 7x15 + 8 is
divided by x - 1.
18

7. QUESTION 6
o Use synthetic division to find each quotient.
a. (3x4 + 9x3 – 9x + 9) ÷ (x – 2)
b. (27x3 – 343) ÷ (-7 + 3x)
a. Q(x) = 3x3 + 15x2 + 30x + 51 and R(x) = 111
b. Q(x) = 9x2 + 21x + 49

8. QUESTION 7
 If 2x3 + Mx2 + Nx + 6 is divisible by both x – 1 and
x + 2, find the value of M and N.
M = -1 and N = 7

9. QUESTION 8
 If x2 – 3x - 3 is divided by x + 4a, the remainder is
7, what is a?
a = -5/4 and 1/2

10. QUESTION 9
 When 15x5 + 5x4 + Bx3 – 2x2 – 23x + 18 is divided
by 3x – 2, the quotient is 5x4 + 5x3 + Ax2 + 4x – 5
and the remainder is 8. Find the values of A and B.
B = 11 and A = 7

11. QUESTION 10
 Find all the real zeros of P(x) = 6x4 + x3 – 13x2 – 2x + 2.
Zeros: {-1/2, 1/3, sq rt. of 2, negative sq rt. of 2