Question 1184612
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The reference provided by the other tutor is, in my opinion, not a particularly good one.  It shows SOLVING several example quadratic equations; but it doesn't provide much explanation on HOW TO SOLVE them.<br>
The instructions for this problem say to solve using "the appropriate method".<br>
It is unclear what "the appropriate" method is; different students will use different methods.<br>
You can ALWAYS solve a quadratic equation using the quadratic formula.  However, the probable intent of this problem is to provide practice in solving by factoring.<br>
So let's take a look at what is involved in solving by factoring.<br>
We want to factor x^2-2x-8 into the form (x+a)(x+b) where a and b are integers.<br>
{{{(x+a)(x+b)=x^2+ax+bx+ab = x^2+(a+b)x+(ab) = x^2-2x-8}}}<br>
We see that our two numbers a and b have to be such that
(1) their sum a+b is -2; and
(2) their product ab is -8<br>
Clearly the product ab=-8 means one of the numbers is positive and one negative.  Then playing around with possible values of a and b to give a product of -8 and a sum of -2 gives us -4 and 2 as the two numbers.  So the factorization is<br>
{{{x^2-2x-8=(x-4)(x+2)}}}<br>