Question

Factor the polynomial completely:
3a^4 - 8a^3 + a^2

Answer 1

Start by pulling out as many a's as possible:

a^2(3a^2-8a+1)

Then look at the inside and notice it is a quadratic equation, which you most likely have factored by itself before:

3a^2-8a+1 = (3a +- ?)(a +- ?)
[I was able to assume that the coefficients of the a's are 3 and 1 because that is the only possible combination that multiplies to 3a^2. This little time-saver works whenever the coefficient of a^2 is a prime number, in which case one of the a's will be the coefficient itself while the other is just 1]

Answer 2

3a^4 - 8a^3 + a^2 = a^2(3a^2-8a+1)
That is it.
The quadratic part does not factor nicely and so you leave it as it is.

Answer 3

I just assumed since it said "factor completely" that it wanted us to use the quadratic formula if necessary

Answer 4

Thanks. This is getting me confused because im always told to first find the GCF, there is none so I'm always stuck after that.

Answer 5

Yes, find GCF first:
3a^4 - 8a^3 + a^2
every term has a^2 as a factor and it is the GCF that can be factored out:
a^2(3a^2 - 8a + 1).
Then see if the quadratic part can be factored. In this case it does not factor and so leave it as it is.