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)?

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:

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.