How do you factor $28x^3 +17x^2 -30x + 6$ ?

Question

1631 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-22T15:04:27

Refer to explanation

Using the following "clever" method

We try to factor it as a product of a polynomial of first degree and one of second degree as follows

$28x^3+17x^2-30x+6=(4x+a)*(7x^2+bx+c)$

Now doing the calculation in the RHS of the equation and equating the correspoding parts we get

$a=-1,b=6,c=-6$ hence

$28x^3+17x^2-30x+6=(4x-1)*(7x^2+6x-6)$

It is easy to factor $7x^2+6x-6$ as well hence we have that

$28x^3+17x^2-30x+6=(4x-1)*[-1/7*(-7x+sqrt51-3)*(7x+sqrt51+3)]$

How do you factor 28x^3 +17x^2 -30x + 628x^3 +17x^2 -30x + 6?