Question

Find the quadratic polynomial that completes the factorization.
u^3 - 27 = (u - 3)

Answer 1

Answer:

$u^2+3u+9$

Step-by-step explanation:

The way to remember it, is like the square of a binomial, but all coefficients are 1.

So it's the square of the first term. The cross product. The square of the second. And you take only one of them.

In our situation is $u^2+3u+9$

If you want a way to find it, the way you think is it. It's a second degree polynomial, so $au^2+bu+c$. Then you multiply the terms together, and you have to get terms removing in a way that you're left with just $u^3-27$. With some number crunching you'll end up with $a=1; b=3, c=9$