ALGEBRA HELP!!!! http://assets.openstudy.com/updates/attachments/51b26e16e4b06ee3ee27cd8e-goldyyy-1370648537248-untitled.jpg

Question

whpalmer4 · Answer

$$x^2+5x-6$$That factors to something like $$(x-a)(x+b)$$Because we have a negative number for the last term of the product, one of our factors will have a negative number and the other a positive number.  Also, the two of them multiplied together will equal -6, but added will equal +5.  Any idea what they might be?

$$(x-a)(x+b) = x^2 + bx - ax -ab = x^2 + (b-a)x - ab$$
We need $b-a=5$ and $-a*b = -6$ if we are going to match up terms between that equation and our original:
$$x^2+5x-6 = x^2+(b-a)x-ab$$

anonymous · Answer

okay but i kinda don't get it

whpalmer4 · Answer

Let's look at where the various pieces come from:

$$(x+a)(x+b) = x^2 + bx + ax + ab = x^2 + (a+b)x + ab$$Right?  
Notice that the first term ($x^2$) comes entirely from multiplying the $x$ terms.  The constant term ($ab$) comes entirely from multiplying the constant terms.  That means if our expression we are factoring ends in 6, the two constant terms multiplied together must be factors of 6.  Agreed?

anonymous · Answer

yes

whpalmer4 · Answer

Okay, now how about the middle term?  That comes from adding together the constant terms, not multiplying them.  We have a negative number for the coefficient of the constant term, so one of the constant terms must be a negative number, right?  But only one, because if both of them were negative, we'd have a positive value for the constant term. (- * - = +)

So, that means that we have to find two numbers that we can multiply together to get -6, but add together to get 5.  What are the factors of -6?  -1*6, -2*3, -3*2, -6*1, 1*-6, 2*-3, 3*-2, 6*-1

Which of those pairs adds to 5?