Math: novelty factoring, part 1

Tutoring math, factoring is a typical topic. The tutor mentions a novelty.

In this post, x^n means xⁿ

Sometimes, one can factor third degree polynomials of the form

ax^3 +bx^2 +cx + d

without using the remainder theorem, synthetic division, etc.

One situation where this is possible is if the first two terms and the second two share a common binomial factor. For instance:

x^3 + 3x^2 – 5x – 15

In this case, the first two terms can be common-factored. Next, the third and fourth:

x^2(x+3) – 5(x+3)

The result:

(x^2 – 5)(x + 3)

Source:

Traverse, Kenneth J. et al. Using Advanced Algebra. Toronto: Doubleday Canada Limited, 1977.