Question

Check all of the possible first steps in factoring a polynomial with four terms.

(a) Factor out a GCF
(b) Factor the difference of cubes
(c) Factor a sum of cubes
(d) Factor a difference of squares
(e) Factor a perfect-square trinomial
(f) Factor by grouping

Answer 1

Find the possible first steps in factoring a polynomial with four terms:

A polynomial is represented as: $y=a{x}^n+b{x}^{n-1}+...+d$.

Let the polynomial of four terms be:

$f\left(x\right)=a{x}^3+b{x}^2-cx+d$

There are only two possible case scenarios for any polynomial of the above form.

1. Two terms have a common GCF. e.g. a and b, with a common GCF; -c and d, with a common GCF
2. a, b, c and d; with a common factor. So, the polynomial can be grouped.

However, the given polynomial is not.

• A difference of cubes
• Sum of cubes
• Difference of squares
• Perfect square trinomial (because it has $4$ terms)

Hence, the only possible first steps are

(a) Factor out a GCF

(f) Factor by grouping