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Nikitich [7]
3 years ago
4

A student divided f(x) = 3x^3 + 3x^2 + 5x - 4 by x + 2 and found the remainder was r = -6. Based on the remainder theorem, what

can be concluded about f (x)?
Mathematics
1 answer:
Ierofanga [76]3 years ago
7 0

Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                    x-(3*x^3+8*x^2+5*x-7)=0 

Step by step solution :Step  1  :Equation at the end of step  1  : x-((((3•(x3))+23x2)+5x)-7) = 0 Step  2  :Equation at the end of step  2  : x - (((3x3 + 23x2) + 5x) - 7) = 0 Step  3  :Step  4  :Pulling out like terms :

 4.1     Pull out like factors :

  -3x3 - 8x2 - 4x + 7  = 

 -1 • (3x3 + 8x2 + 4x - 7) 

Checking for a perfect cube :

 4.2    3x3 + 8x2 + 4x - 7  is not a perfect cube 

Trying to factor by pulling out :

 4.3      Factoring:  3x3 + 8x2 + 4x - 7 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  3x3 - 7 

Group 2:  8x2 + 4x 

Pull out from each group separately :

Group 1:   (3x3 - 7) • (1)

Group 2:   (2x + 1) • (4x)

Step-by-step explanation:

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Step-by-step explanation:

I got this answer from somewhere else. but it is correct. i hope this helped.

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3 years ago
Ask Your Teacher The circumference of a sphere was measured to be 90 cm with a possible error of 0.5 cm. (a) Use differentials t
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Answer:  

a)  28,662 cm²  max error

    0,0111     relative error

b) 102,692 cm³  max error

   0,004     relative error

   

Step-by-step explanation:

Length of cicumference is: 90 cm

L = 2*π*r

Applying differentiation on both sides f the equation

dL  =  2*π* dr    ⇒  dr = 0,5 / 2*π

dr =  1/4π

The equation for the volume of the sphere is  

V(s) =  4/3*π*r³     and for the surface area is

S(s) = 4*π*r²

Differentiating

a) dS(s)  =  4*2*π*r* dr    ⇒  where  2*π*r = L = 90

Then    

dS(s)  =  4*90 (1/4*π)

dS(s) = 28.662 cm²   ( Maximum error since dr = (1/4π) is maximum error

For relative error

DS´(s)  =  (90/π) / 4*π*r²

DS´(s)  = 90 / 4*π*(L/2*π)²      ⇒   DS(s)  = 2 /180

DS´(s) = 0,0111 cm²

b) V(s) = 4/3*π*r³

Differentiating we get:

DV(s) =  4*π*r² dr

Maximum error

DV(s) =  4*π*r² ( 1/  4*π*)   ⇒  DV(s) = (90)² / 8*π²

DV(s)  =  102,692 cm³   max error

Relative error

DV´(v) =  (90)² / 8*π²/ 4/3*π*r³

DV´(v) = 1/240

DV´(v) =  0,004

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