P(x) = x3 + 4x2 + 3x – 2 find all

≓4.724576697

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Step by Step Solution:

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Step by step solution :

STEP

1

:

Equation at the end of step 1

(((x3) - 22x2) - 3x) - 2 = 0

STEP

2

:

Checking for a perfect cube

2.1 x3-4x2-3x-2 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3-4x2-3x-2

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

Group 1: -3x-2

Group 2: x3-4x2

Pull out from each group separately :

Group 1: (3x+2) • (-1)

Group 2: (x-4) • (x2

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!