Question 181392
Use synthetic substitution to find: 
{{{f(-4)}}} for {{{f(x)=x^3+3x^2-5x-7}}}
<pre><font size = 4 color = "indigo"><b>
There are two ways to substitute a number for x 
in a polynomial:

1. Direct substitution  (a harder method)

{{{f(x)=x^3+3x^2-5x-7}}}

Replace x by -4

{{{f(-4)=(-4)^3+3(-4)^2-5(-4)-7}}}

{{{f(-4)=(-4)(-4)(-4)+3(-4)(-4)-5(-4)-7}}}

{{{f(-4)=-64+48+20-7}}}

{{{f(-4)=-3}}}

So the answer is -3.  However that's by
direct substitution.  That's not what you
are supposed to do.  You are to use 
synthetic substitution, which is easier.

2. Synthetic substitution. (easier)

{{{f(x)=x^3+3x^2-5x-7}}}.  Put the {{{-4}}}
on the left of a synthetic division array:

-4|1   3   -5   -7
  |<u>   -4    4    4</u>
   1  -1   -1   -3

The answer is the number on the bottom
right, the -3, so

f(-4) = -3 

Notice that you get -3 either by direct
substitution and by synthetic substitution.

Edwin</pre>