Question 1164256
<pre>

The other method is fine if you have memorized the binomial expansion
identity:

(x + y)³ = x³ + 3x²y + 3xy² + y³

and observe how close it is to the given cubic polynomial.  But most
students probably haven't memorized this.  So I did it the other way:

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{{{a^3+3a^2+3a+2}}}

We search for rational roots which are ± factors of 2,
which are ±1, ±2

There are no sign changes so there are no positive roots,
So the only rational roots, if any, are -1 and -2

We try -1

-1 | 1  3  3  2
   |<u>   -1 -2 -1</u> 
     1  2  1  1

No, for the remainder is not 0.

We try -1

-2 | 1  3  3  2
   |<u>   -2 -2 -2</u> 
     1  1  1  0

Yes, for the remainder is 0.

We divided by a+2 and the quotient is determined by
the first three numbers on the bottom of the synthetic
division.  The quotient is 1a² + 1a + 1 or a² + a + 1.

(a + 2)(a² + a + 1)      <--answer

Edwin</pre>