Answer :

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:

Since  [tex]f(x)=3x^3 + 3x^2 + 5x - 4[/tex]  gives a remainder of r = -6 when divided by x + 2, we can conclude that x + 2 is not a factor of f(x)

The given polynomial function is:

[tex]f(x)=3x^3 + 3x^2 + 5x - 4[/tex]

If the function [tex]f(x)=3x^3 + 3x^2 + 5x - 4[/tex] is divided by x + 2, it will give a remainder of r = -6.

The remainder theorem states that when a polynomial f(x) is divided by a linear function x - c to give a quotient q(x) and a remainder r(x), then the following relationship exists.

f(x) = (x-c)·q(x) + r(x)

Since  [tex]f(x)=3x^3 + 3x^2 + 5x - 4[/tex]  gives a remainder of r = -6 when divided by x + 2, it means x + 2 is not a factor of f(x)

Learn more here: https://brainly.com/question/15080015

Other Questions