Monday, October 14, 2013

Remaindor Theorem



1.     If F(x) = 2x + 8/x2, calculate F(2) and F(-2)

2.     If F(x) = -12/x2, calculate F(2)

3.     If P(x) = 2x3 + 3x2 -3x -2 evaluate P(1) and P(-2)

4.     If P(x) = x3 –x2 + 2x + 4 evaluate P(-1) and P(2)

5.     If P(x) = ax3 + bx2 -3x -2 and P(1) = 0 and P(-2) = 0, find the values of a and b.

6.     If P(x) = x3 –x2 + ax + b and P(-1) = 0 and P(2) = 12, find the values of a and b.

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15 comments:

  1. UnknownOctober 14, 2013 at 4:54 PM

    f(2)= 2(2)+8/(2)^2=6
    F(-2)= 2(-2)+8/(-2)^2=-2

    ReplyDelete
  2. UnknownOctober 14, 2013 at 5:07 PM

    f(2)= -12/(2)^2=-3

    3. P(1)= 2(1)^3+3(1)^2-3(1)-2= 0
    P(2)= 2(-2)^3+3(-2)^2-3(1)-2= 0

    4. P(1)= (-1)^3-(-1)^2+2(-1)+4=0
    P(2)= (2)^3-(2)^2+2(2)+4=12

    ReplyDelete
  3. Damian Felix October 17, 2013 at 3:59 PM

    This comment has been removed by the author.

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  4. Damian Felix October 17, 2013 at 4:06 PM

    F(2) = 2(2)+ 8/(2)^2
    = 4+2
    F(2) = 6


    F(-2) = 2(-2) + 8/(-2)^2
    = -4+2
    F(-2) = -2

    ReplyDelete
  5. UnknownOctober 19, 2013 at 4:37 PM

    This comment has been removed by the author.

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  6. UnknownOctober 19, 2013 at 5:03 PM

    1. 2x + 8/x^2

    8/x^2 ==> 8x^ -2

    f(2)= 2(2) + 8(2)^ -2
    = 4 + 0.25
    = 4.25

    f(-2)= 2(-2) + 8(-2)^ -2
    = -4 - 0.25
    = -4.25

    2. -12/x^2 ==> -12x^ -2

    f(2)= -12(2)^ -2
    = -12(0.25)
    = -3

    3. P(x) = 2x^3 + 3x^2 -3x -2
    P(1)= 2(1)^3 + 3(1)^2 - 3(1) - 2
    = 0
    P(-2)= 2(-2)^3 + 3(-2)^2 - 3(-2) - 2
    = 0

    4. P(x) = x^3 –x^2 + 2x + 4
    P(-1)= (-1)^3 - (-1)^2 + 2(-1) + 4
    = 0
    P(2)= (2)^3 - (2)^2 + 2(2) + 4
    = 12

    5. P(x) = ax^3 + bx^2 -3x -2
    P(1) = a(1)^3 + b(1)^2 -3(1) -2
    0 = a + b - 3 -2
    3+2 = a + b
    5 = a +b <== eq 1

    P(-2) = a(-2)^3 + b(-2)^2 -3(-2) -2
    0 = -8a + 4b + 6 -2
    -6 +2= -8a + 4b
    -4 = -8a + 4b
    -2 = -4a + 2b <== eq 2
    From eq1 5-b=a
    sub in eq 2 -2 = -4a + 2b
    -2 = -4 (5-b) + 2b
    -2 = -20 + 4b +2b
    -2 +20= 6b
    18 = 6b
    3 = b
    5= a +3
    5 - 3 = a
    2 = a ==> b=3 a=2

    ReplyDelete
  7. KonOctober 20, 2013 at 6:26 PM

    1) F(2) = 6
    F(-2) = -2

    2) F(2) = -3

    3) P(1) = 0
    P ( -2) = 32

    4) P(-1) = 0
    P (2) = 12

    5) a = -2
    b = 7

    6) a = 3.3
    b = 5.3

    ReplyDelete
  8. UnknownOctober 21, 2013 at 2:24 PM

    1)
    f(x)= 2[x] + 8/[x]^2

    f(-2) = 2[-2] + 8/ [-2]^2
    = -4 + 8/ [-4]
    = -4 + 2
    = -2
    f(2)= 2[2] + 8/ [2]^2
    = 4 + 8/4
    = 4 + 2
    = 6

    ReplyDelete
  9. UnknownOctober 21, 2013 at 2:29 PM

    2) f(x)= -12/x^2

    F(2)

    = -12/[2]^2

    = -12/4

    = -3

    ReplyDelete
  10. UnknownOctober 21, 2013 at 2:45 PM

    p(x)= 2[x]^3 + 3[x]^2 - 3[x] - 2

    p(-2)= 2[- 2]^3 + 3[-2]^2 - 3[-2] - 2

    = - 16 - 12 + 6 -2

    = 0

    p(1)= 2[1]^3 + 3[1]^2 - 3[1] -2

    =2 + 3 - 3 -2

    = 0

    ReplyDelete
  11. UnknownOctober 21, 2013 at 3:05 PM

    4) p[x] = x^3 -x^2 + 2x + 4

    p(-1)=

    [-1]^3 - [-1]^2 + 2[-1] + 4

    = -1 -1 -2 +4

    = 0

    p[2]= [2]^3 - [2]^2 + 2[2] + 4

    = 8 - 4 + 4 + 4
    = 12

    ReplyDelete
  12. UnknownOctober 21, 2013 at 3:39 PM

    p[x]= ax^3 +bx^2- 3x-2

    p(1)=0

    =a[1]^3 + b[1]^2 - 3[1] - 2

    = a + b - 3 -2

    =a + b - 5

    = a + b = 5 ep 1

    p[-2]= a[-2]^3 + b[-2]^2 -3[-2] - 2

    =-8a + 4b + 6 - 2

    =-8a + 4b + 4

    = -8a + 4b = -4 eq 2

    a + b = 5 in eq 1 make b the subjt
    b= 5-a

    -8a + 4b = -4 eq 2

    -8a + 4(5-a) = -4 subs b into eq 2

    -8a + 20 - 4a = -4

    -12a + 20 = -4

    a= -4-20/[-12]

    =2

    a+b=5 subs a into eq 1

    (2) + b=5

    b=5-2

    =3


    a= 2 b= 3

    ReplyDelete
  13. UnknownOctober 21, 2013 at 4:18 PM

    p[x]= x^3 + x^2 + ax + b

    p[2]=12

    [2]^3 - [2]^2+ a[2] + b = 12

    8 - 4 + 2a + b = 12
    4+ 2a + b =12
    2a + b = 12-4
    2a+b=8 eq1

    p[-1]

    [-1]^3 - [-1] ^2 + a[-1] +b
    -1+1-a+b
    a-b=-2 eq 2

    2a + b = 8 eq 1

    a-b= -2 eq 2
    a=-2+b make a the subjt of eq 2

    2a + b= 8 sub a into eq 1

    2[-2+b]+b=8

    -4+2b+b=8

    3b=8+4

    b=12/3

    =4

    a-b= -2 subs b into eq 2

    a - 4= -2

    a=-2+4

    =2


    a=2 b = 4

    ReplyDelete

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