Question 1207728
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It sounds like you want to factor this polynomial.


You have the right idea, but your line of thinking only works if the leading coefficient is 1.


Unfortunately the leading coefficient is 3 instead.


Multiply the leading coefficient with the last term.
3*(-2) = -6


The task of factoring this will have us look for a pair of numbers that
Multiply to -6 AND that add to -5


Let's look at all of the ways to multiply to -6 using two integers (which I'll call m and n).
<table border = "1" cellpadding = "5"><tr><td>m</td><td>n</td><td>m+n</td></tr><tr><td>-6</td><td>1</td><td>-5</td></tr><tr><td>-3</td><td>2</td><td>-1</td></tr><tr><td>-2</td><td>3</td><td>1</td></tr><tr><td>-1</td><td>6</td><td>5</td></tr></table>
The first row of this table shows that
-6 * 1 = -6
-6 + 1 = -5
The table is entirely optional. You can find these m,n values through trial-and-error. 


Anyways the mystery pair of numbers we want are -6 and 1.
So we'll break the middle term -5p into -6p+1p and apply factor by grouping.


3p^2-5p-2
3p^2-6p+1p-2
(3p^2-6p) + (p-2)
3p(p-2) + 1(p-2)
(3p+1)(p-2)


We've shown that 3p^2-5p-2 fully factors to (3p+1)(p-2) 


You can use the FOIL rule to expand (3p+1)(p-2) back to the original expression as a way to verify the answer.
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