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)
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