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How do you factor #y= 3x^7 - 9x ^6 + 18x ^5#?

Answer 1

Hazel Anglin

#y = 3x^7-9x^6+18x^5=3x^5(x^2-3x+6)#

First note that all the terms are divisible by #3x^5#, so separate that out as a factor:

#y = 3x^7-9x^6+18x^5=3x^5(x^2-3x+6)#

The remaining quadratic factor is in the form #ax^2+bx+c# with #a=1#, #b=-3# and #c=6#.

This has discriminant #Delta# given by the formula:

#Delta = b^2-4ac = (-3)^2-(4xx1xx6) = 9-24 = -15#

Since this is negative, the quadratic has only Complex zeros and cannot be factored any further with Real coefficients.

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Answer 2

Julia Adams

To factor the expression y = 3x^7 - 9x^6 + 18x^5, you can factor out the greatest common factor, which is 3x^5, to get: y = 3x^5(x^2 - 3x + 6).

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Answer from HIX Tutor

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