Expert: Richard J. Raridon - 6/14/2011

Question
1) Find the remaining roots for the following equation:
2x3 - x2 + 10x - 5 = 0; iÖ5

2) Find f(c) for the given polynomial f(x) and value c:
f(x) = 3x3 + 8x2 - 6x + 4; c = -4

3)   Divide:
2x4 - x3 + x2 + 4x - 4
-----------------------
    2x2 + x - 2
4)Divide:
2a3 + 8a2 - 3a + 8
------------------
       a + 4
5)Divide:
4u^4-4u^3-5u^2-9u-1
-------------------
       2u-1    
6)Solve for n:
Ö4n - 8   = 10

7)Solve for n:
Ö2n + 4   =6

8)Solve for n:  
Ö5n + 6   = n
9)Solve for w:
w^2/4+7w/4 =1
10)Solve:
|a/2+1| = 3
11) x+1/-x+2= 2/x
12)Solve given the root indicated:
Equation:  x4-5x2-10x-6=0
Root:-1+i
13)Determine the missing roots:
Equation:  x4-3x3+4x2-6x+4=0
Roots:   
1,2,iÖ2
14)Find an equation with integral coefficients that has the given roots:
1,-3,-4
15)Solve given the two roots:
2x^4-5x^3-11x^2+20x+12;-2,3
16)Find a polynomial equation with integral coefficients that has the roots:
1,-1.5,2
17)Find a polynomial equation with integral coefficients that has the roots:
-2,-i,i
18)Find a polynomial equation with integral coefficients that has the roots:
-2,2,-3
19)Solve using the given root:
2z^3+z^2-8z+3=0;1.5
20)Solve using the given root:
2x^3+9x^2+7^x-6=0;-2
21)Find the remainder when z + 2 is divided into
P(z)=z^5+2z^4+z^3+2z^2+z+2
22)Find the remainder when t + 1 is divided into
P(t)=t5+t4+t3+t2+t+1
23)Use synthetic substitution to find P(c) for the given polynomial P(x) and the given number x:
P(x)=6x^3-x2^+4x+3;c=-0.33
24)Use synthetic substitution to find P(c) for the given polynomial P(x) and the given number x:
P(x)=1-7x-4x^2+x^3;c=6
25)Use synthetic substitution to find P(c) for the given polynomial P(x) and the given number x:
P(x)=x^3+4x^2-8x-6;c=-5
26)Use synthetic substitution to find P(c) for the given polynomial P(x) and the given number x:
P(x)=4x^3-2x^2+x-1;c=-0.5

Answer
1. Learn to make square roots as i(5^1/2) and, of course, imaginary roots always come in pairs so you have x = -i(5^1/2) and 1/2
2. 348
3. x^2-x+2
4. cannot divide
5. cannot divide
6. I presume you mean (4n-8)^1/2 = 10 so n = 27
7. (2n+4)^1/2 = 6 so n = 16
8. n = -1,6
9. w = [-7 +/-(65)^1/2]/2
10. a = 4 or -8
11. I presume you mean (x+1)/(-x+2) = 2/x so x = 1, -4
12. x = -1-i, 3,-1
13. -i(2^1/2)
14. x^3+6x^2+5x-12
15. x = 2, -1/2
16. 2x^3-3x^2-5x+6
17. x^3+2x^2+x+2
18. x^3+3x^2-4x-12
19. 1 +/-(2^1/2)
20. x = -3, 1/2
21. 0
22. 0
23. 4/3
24. 31
25. 9
26. -5/2