Question 166180
1. You don't need synthetic division to find f(-3). Just substitute.
{{{f(x)=2x^3-6x^2-5x+7}}}
{{{f(-3)=2(-3)^3-6(-3)^2-5(-3)+7}}}
{{{f(-3)=2(-27)-6(9)+15+7}}}
{{{f(-3)=-54-54+15+7}}}
{{{f(-3)=-86}}}
.
.
.
2. Here you need the synthetic division.
Showing synthetic division is a little difficult.
The first part will show the factor (left hand column), then the factor times the divisor,
then the next line will show the subtraction.
Repeat.
Hopefully it makes sense.
.
.
.
..........._______________
(x+4)|x^3+x^2-22x-40 
x^2:...x^3+4x^2
..................-3x^2-22x-40
-3x:..........-3x^2-12x
.............................-10x-40
-10:......................-10x-40

{{{x^3+x^2-22x-40=(x+4)*(x^2-3x-10)}}}
Now you can factor the quadratic,
{{{x^2-3x-10=(x-5)(x+2)}}}
and substitute back,
{{{x^3+x^2-22x-40=(x+4)*(x-5)*(x+2)}}}