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please help explain this lesson

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The simplest form is probably this one:

"If the remaining trinomial is still of the form ax2 + bx + c, find two integers, r and s, whose sum is b and whose product is ac. Then rewrite the trinomial as ax2 + rx + sx + c and use grouping and the distributive property to factor the polynomial."

I.e. 6x^2 - 8x -30 has ac=-180 and b=-8.  So r=10 and s=-18 works.

Now you get 6x^2 + 10x - 18x - 30 which is (3x+5)(2x-6).

(Note that we could have first divided everything by 2 to make the numbers smaller.)
 
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Are you talking about things like

6x^(2) \- 8x - 30 = (3x + 5) (2x - 6) ?

Are you supposed to be using the quadratic formula, or "completing the square", or are you supposed to be just winging it?

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