How do I factor 4x^2+18x-10? Can this be factored or not?

How do I factor 4x^2+18x-10?

Yes, it can be factored. I would start by factoring out the common factor of 2, then use whatever method you are familiar with for factoring a trinomial.

If you need help with that, please show your work as far as you get, so we can see your method and guide you along.
 
Yes, it can be factored. I would start by factoring out the common factor of 2, then use whatever method you are familiar with for factoring a trinomial.

If you need help with that, please show your work as far as you get, so we can see your method and guide you along.

2x + 9x -5, box method won't work.
 
First of all it is: \(\displaystyle 2x^2+9x-5\).

a=2, b=9, c=-5

so find two numbers that add to give b=9 and multiply to give ac=-10

Is this what you mean by the "box method"?

b=9ac=-10
10 + -1 =910*-1=-10

These two numbers are used to break up the middle term:
\(\displaystyle 2x^2+9x-5\)

=\(\displaystyle 2x^2+ 10x +-1x -5\) ...break up the middle term

=(2x^2+ 10x) +(-1x -5) …..put pairs in brackets

=2x(x + 5) +-1(x +5) ….factorise each pair

=(x + 5)(2x -1) … factorise completely

ALWAYS check your answer by expanding:
(x + 5)(2x -1) =2x^2 -x +10x - 5 = 2x^2 +9x -5. All good!!

(This is an ok method when you are first starting out. There are quicker methods.)
 
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Is this what you mean by the "box method"?

I just googled Box Method Factoring and learned what it is: https://www.purplemath.com/modules/factquad2.htm .

I had heard the term but never looked it up before; it turns out to be more or less equivalent to the "ac grouping" method I am familiar with.

But the next page, https://www.purplemath.com/modules/factquad3.htm, shows how an example with a common factor can lead to confusion, which may be part of what happened here.
 
2x + 9x -5, box method won't work.
Why not? That method says that you need factors of (2)(-5) = -10 that will add up to +9. Since you're multiplying to a negative, one factor will be positive and one will be negative. Since you're adding to a positive, the larger factor (in absolute-value terms) will get the "plus" sign, and the factors will need to be nine units apart.

Here are the factor pairs:

. . . . .-1 and +10
. . . . .-2 and +5

Are you sure that neither option will work? ;)
 
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