4TH QUARTER LONG TEST REVIEW

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

QUESTION 2

Determine the center and the radius of the circle x2 + y2 + 4y + 10x = -4.

C(-5, -2), r = 5

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

QUESTION 4

What polynomial will have a quotient of 3x3 + 2x -1 when divided by x - 3.

3x4 – 9x3 + 2x2 – 7x + 3

QUESTION 5

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

18

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) = 111b. Q(x) = 9x2 + 21x + 49

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

QUESTION 8

If x2 – 3x - 3 is divided by x + 4a, the remainder is 7, what is a?

a = -5/4 and 1/2

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

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