how do i factor:
f(x) = 3x^3 - 12x^2 - 15x

Question

how do i factor:
f(x) = 3x^3 - 12x^2 - 15x

whpalmer4 · Answer

Well, first I would simplify the polynomial by noting that all three coefficients are multiples of 3, so divide them all by 3, giving
$$f(x) = 3(x^3-4x^2-5x)$$There's also an x in each term that can be factored out$$f(x)=3x(x^2-4x-5)$$

Now to factor $$x^2-4x-5$$Remember that $$(x+a)(x+b) = x^2+bx + ax + ab = x^2 + (a+b)x + ab$$We've got that same form, if we let (a+b) = -4 and ab = -5.  Figure out two numbers that fit that constraint, and you're done!

whpalmer4 · Answer

Our final factoring would be
$$f(x) = 3x(x+a)(x+b)$$

anonymous · Answer

so would 3x(x-4) (x+1) work?

whpalmer4 · Answer

Close!  What is (x-4)(x+1)?  x^2-4x + x - 4 = x^2 -3x -4
Hint: -4*1 = -4, not -5 :-)

anonymous · Answer

so its x(-5) (x+1) right?

whpalmer4 · Answer

Yep!  Full factorization is $$f(x)=3x(x-5)(x+1)$$ and if f(x) = 0, it will have solutions at x = 0, x = 5, x = -1.

anonymous · Answer

yep thanks so much!