Find the complete factored form of
-25a^6 + 10a^5 + 45a^4

Question

Find the complete factored form of 
-25a^6 + 10a^5 + 45a^4

whpalmer4 · Answer

Are there any common factors to the coefficients?  If so, factor them out by using the distributive property in reverse: ab + ac + ad = a(b+c+d)

Are there any common factors to the rest of the terms?  Again, if so, factor them out.

It may be helpful as a learning exercise to write it out as its factors.  For example, 

$$3x^2 + 6x = 3*x*x + 2*3*x = 3*(x*x + 2*x) = 3*x*(x+2) = 3x(x+2)$$

whpalmer4 · Answer

Last line got cut off, it should end with
$$= 3x(x+2)$$

anonymous · Answer

I think I got it, thanks!

whpalmer4 · Answer

What's your answer?

anonymous · Answer

5a^4 (-5a^2 + 2a + 9)

anonymous · Answer

I don't think that's complete though...

whpalmer4 · Answer

Okay, that's correct so far, but your instinct that we need to factor the trinomial $-5a^2 + 2a + 9$ is a good one.  Do you know to do that?

whpalmer4 · Answer

As it turns out, while the instinct is good, in this case the trinomial can't be further factored into a product of terms such as $$(-5a + 7)(a + 1)$$ (which would give us $-5a^2-5a+7a +7 = -5a^2+2a+7$ if expanded—close, but no cigar!)