The first term is, <span> <span>3p2</span> </span> its coefficient is <span> 3 </span>.
The middle term is, <span> -2p </span> its coefficient is <span> -2 </span>.
The last term, "the constant", is <span> -5 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 3</span> • -5 = -15</span>
Step-2 : Find two factors of -15 whose sum equals the coefficient of the middle term, which is <span> -2 </span>.
<span><span> -15 + 1 = -14</span><span> -5 + 3 = -2 That's it</span></span>
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 3
<span>3p2 - 5p</span> + 3p - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
p • (3p-5)
Add up the last 2 terms, pulling out common factors :
1 • (3p-5)
Step-5 : Add up the four terms of step 4 :
(p+1) • (3p-5)
Which is the desired factorization
Final result : (3p - 5) • (p + 1)
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