We are given 5x^2+2x-3 and told to factor it.
To factor this, we must find the value that multiplies to -15 and adds to 2. The only numbers that multiply to -15 are +-(1*15) and +-(3*5). Out of those, only -3+5 adds to 2.
So now we have our vaues, now we just have ot factor it. I'm going to use the factor by grouping method, which is where I re write the problem color(blue)(5x^2)+2xcolor(green)(-3) as (color(blue)(5x^2)+color(white)(...))+(color(white)(...)color(green)(-3)). We fill in the blanks with our -3 and 5, though we add and x when we put them into the parenthathes, like this: (color(blue)(5x^2)+5x)+(-3xcolor(green)(-3)). It doesn't matter where the -3 and 5 goes, but I put them in this way because it's the easiest to factor. If we factor them, we get 5x(x+1)+color(white)(.)-3(x+1). We can simplify this to (5x-3)(x+1). And that's it. Nice job!
