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

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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)]#