how do you factor this completely? 20x3 + 12x2 + 5x + 3

Question

anonymous · Answer

the numbers by the X's are the exponents

anonymous · Answer

(20x^3 + 12x^2)(5x + 3)
Factor out a 4x^2 from the first parentheses ->
4x^2(5x + 3)(5x + 3)
What you want to to is make sure the stuff inside both parentheses is the same. Since 5x + 3 is in both parentheses, we can move on to the next step.
Whatever you factored out of the parentheses goes into a 'factor' by itself. 
So (4x^2)(5x + 3) is what we have now.
We can further factor 4x^2 into (2x)(2x)
The factors of this equation are thus (2x)(2x)(5x + 3), which can be written also as (2x)^2(5x + 3).
As a rule of thumb, the greatest exponent you have on your x indicates the number of factors you will have for the polynomial. If it was x^4 + x^3 + ..., then you would have four factors. If it was x^2 + x + ..., you would have two factors.