Question 1183223
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You can always factor a quadratic expression using the quadratic formula; it is not as much work as the first tutor makes it look.<br>
The solution by the second tutor is fine.  But it doesn't teach YOU how to factor the quadratic.  For this example, replacing 3x with 4x-x makes the expression factorable using grouping -- but you have no way of knowing that "4x-x" is how you want to replace the "3x".  So for a student wanting to learn how to factor the expression, that solution is of little use.<br>
There are many well-defined methods for factoring quadratics.  I am definitely old school on this and think the best way to learn to factor quadratics is by looking at the possible factorizations and finding the one that is right.<br>
We want to have<br>
{{{2x^2+3x-2 = (ax+b)(cx+d)}}}<br>
To get the leading term 2x^2, a and c have to be, in some order, 1 and 2.
To get constant term -2, b and d have to be, in some order, 1 and -2, or -1 and 2.<br>
Look at all the possible factorizations and find the one that gives the correct linear term "3x".<br>
(2x+1)(x-2)
(2x-1)(x+2)
(2x+2)(x-1)
(2x-2)(x+1)<br>
Before actually calculating the middle term for each of these possible factorizations, we can rule out the last two.  In each of those, the first factor has a common factor of 2, which means the resulting quadratic would have a common factor of 2 -- but it doesn't.  So the correct factorization is one of the first two.<br>
The first one gives a middle term of -3x, which is the right size but wrong sign; the second one gives us the correct middle term.<br>
ANSWER: {{{2x^2+3x-2 = (2x-1)(x+2)}}}<br>