How do you factor #4y=x^3-4x^2-11x+30 #?
1 Answer
Sep 2, 2016
Explanation:
By the rational roots theorem, any rational zeros of
That means that the only possible rational zeros are:
#+-1, +-2, +-3, +-5, +-6, +-10, +-15, +-30#
If
#x^3-4x^2-11x+30 = (8)-4(4)-11(2)+30 = 8-16-22+30 = 0#
So
#x^3-4x^2-11x+30 = (x-2)(x^2-2x-15)#
To factor the remaining quadratic, find a pair of numbers with difference
#x^2-2x-15 = (x-5)(x+3)#
Putting it all together, we have:
#4y = (x-2)(x-5)(x+3)#