Could someone please assist me on factoring this problem?

Question

2x^2+5x-3

Answer 1

This type of equation is known as an ax^2 + bx + c.

There is more than one way to go about solving this problem. One way is to try out different possibilities and check by expansion:

We look first at the two possible first terms. They will, in this case, HAVE to be (2x + ___)(x + ____) because 2x * x is the only thing that will give 2x^2.

So then it's a matter of filling those blanks with numbers who have a product of -3, that c in the equation. Fortunately, there aren't a lot of options: -1 and 3, 1 and -3, 3 and -1, -3 and 1. You can use mental math or actually expand the whole thing to discover that it would be -1 and 3:
(2x - 1)(x+3)

Expanded, that would give us 2x^2 + 6x - x - 3 which, simplified, is 2x^2 +5x - 3.

Another way to do this is this:

You figure out the two numbers whose product is a*c and whose sum is 5. a*c in this case is 2 * -3, or -6. If your mental math is good, you'll see right away that you need 6 and -1. We are actually going to use these as 6x and -x to replace the +5x and rewrite the question:

2x^2 + 6x - x - 3

Now I'm going to group the question a bit:

(2x^2 + 6x) + (-x - 3)

I'm now going to pull out any common factors:

2x(x + 3) + -(x + 3), keeping in mind that I've actually pulled out -1 from that second set of brackets.
See how both the part before the + has (x+3) and so does the part after the + ? That is a common factor for both terms. If we pull that out, we're left with:

(x+3)(2x-1)

This second way makes a lot of sense if you've already had practice grouping and factoring after the grouping.

There is also a box method. You can read more about that here: http://www.purplemath.com/modules/factquad2.htm

Answer 2

when factoring, if the problem has x^2 you know that there is an x in the parentheses. so you would have (2x...)(x...). now you should look at the number if there is one, in this case the number is -3, so that means that one of the values in the parentheses is negative. the combinations are either, (2x+3)(x-1) or (2x-1)(x+3). The factored form of the problem would be (2x-1)(x+3) because if you distribute the numbers you get 2x^2 +6x -1x-3, which is the same as 2x^2+5x-3.

Answer 3

(x+3)(2x-1)
x=-3 , 1/2

Answer 4

(2x-1)(x+3)=0

Answer 5

(2x-1 )(x+3)