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!
