Quandaries
and Queries 

Hi! Just wanted to say your site is really helpful. I am trying to figure out some quadratics and I think I've got it, but this one question I have just isn't working. Here it is: 6x+8=x^{2} and so far I have: 6x+8=x^{2} But heres the problem... when I check my answer it says my points should be (2,4). So what am I doing wrong? I have check the book soo many times to see if I am copying the question right and I am. Also, I was wondering how you know which point comes first? Thanks! 

Hi Jess, Right. So far, you factored the polynomial x^{2}+6x+8 as the product (x+4)(x+2). If the question is to solve the equation x^{2}+6x+8 = 0, that is, find the values of x for which the equation x^{2}+6x+8 = 0 is true, then your factorization is useful, because it reduces the question to solving the equation
and A PRODUCT IS ZERO IF AND ONLY IF ONE OF THE FACTORS IS ZERO. Hence you only need to solve x+4 = 0, and you find x = 4, and x + 2 = 0, and you find x = 2; hence the two answers are x = 2 and x=4, and this is what the answer key says. Claude 

