Write the polynomial in factored form.

4x3 + 8x2 – 96x

Question

Write the polynomial in factored form.

4x3 + 8x2 – 96x

anonymous · Answer

I need someone to explain to me how to do this.

e.mccormick · Answer

$4x^3 + 8x^2 – 96x$

OK, you want things to add up, but one od the simple thing to look at first is if you can factor out a constant.

anonymous · Answer

you can't, right?

e.mccormick · Answer

Well, they are eve so you have to be able to factor out a 2, and possibly a 4.

e.mccormick · Answer

What do you get if you try to factor out a 4?

e.mccormick · Answer

And an x, since there is at least one x in each term.

anonymous · Answer

2 and 4 and 48? is that what you mean?

anonymous · Answer

4x3+8x2-96x=4x(x2+2x-24)
=4x(x2+6x-4x-24)
=4x{x(x+6)-4(x+6)}
=4x(x+6)(x-4)

anonymous · Answer

ok I can kinda see where that came from

e.mccormick · Answer

Well, that would be if you factored out a 2.  But if you factor out the 4, you get 1, 2, and -24.  But surjit has just posted all the steps....

anonymous · Answer

thanks

e.mccormick · Answer

Have any questions on how that was done?

anonymous · Answer

not really sure were 24 came from

e.mccormick · Answer

96/4

e.mccormick · Answer

25*4=100.  and 96 is 4 less than 100, so 24*4=96.

anonymous · Answer

and 8/4?

e.mccormick · Answer

Is the 2.

anonymous · Answer

and 4/4 is the x^2 i think i get it

e.mccormick · Answer

Yah, that is the way to factor out from all of them.  Find something that divides out of all the terms.  Then you separate it with () because it would multiply back to all the terms.

anonymous · Answer

gotchya thanks

e.mccormick · Answer

np.  Have fun!