1
$\begingroup$

Just to be upfront, this is a homework question, I already know the answer, but I can't figure out how to get there or the logic behind the hint, which is really what I'm after. Please don't solve it for me, just give me some pointers in the right direction or links to better instructions.

The problem:

Factor the expression $x^3 - 3x^2 + 4$

The hint the book provides "subtract and add 1, then factor by grouping"

The given answer is $(x+1)(x-2)^2$

$\endgroup$
  • $\begingroup$ $-3x^2=x^2-4x^2$ $\endgroup$ – Peđa Terzić Oct 25 '11 at 17:35
  • $\begingroup$ @pedja is that what they mean by subtract and add 1? $\endgroup$ – Marshall Brekka Oct 25 '11 at 17:41
  • 1
    $\begingroup$ no,they mean: $(x^3+1)+(-3x^2+4-1)$ $\endgroup$ – Peđa Terzić Oct 25 '11 at 17:48
  • $\begingroup$ If you don't see it otherwise, you can try the rational root theorem, saying that any rational roots for this polynomial are among $\pm 1, \pm 2, \pm 4$. Once you find one that works, divide it out and you have a quadratic. $\endgroup$ – Ross Millikan Oct 25 '11 at 17:49
  • $\begingroup$ @Marshall, pedja yes because you are just writing 3 as (4-1) in front of $x^2$, precisely 3=$(3+1)-1$ :) $\endgroup$ – Tapu Oct 25 '11 at 17:50
4
$\begingroup$

HINT

$x^3 - 3x^2 + 4 = x^3 + 1 -3x^2 + 3 = (x + 1)(...) - 3(x^2 - 1) = ...$

| cite | improve this answer | |
$\endgroup$
  • 1
    $\begingroup$ Then you'll use the "sum of cubes" and "difference of squares" formula. $\endgroup$ – The Chaz 2.0 Oct 25 '11 at 17:54
1
$\begingroup$

Hint: use @pedja,s hint (this is the best, I can think of).

Else, split $4$ as $4=3+1$ and go through a longer route.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.