Factoring <span> x2-13x+40</span>
The first term is, <span> <span>x2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> -13x </span> its coefficient is <span> -13 </span>.
The last term, "the constant", is <span> +40 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 1</span> • 40 = 40</span>
Step-2 : Find two factors of 40 whose sum equals the coefficient of the middle term, which is <span> -13 </span>.
<span><span> -40 + -1 = -41</span><span> -20 + -2 = -22</span><span> -10 + -4 = -14</span><span> -8 + -5 = -13 That's it</span></span>
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and -5
<span>x2 - 8x</span> - 5x - 40
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-8)
Add up the last 2 terms, pulling out common factors :
5 • (x-8)
Step-5 : Add up the four terms of step 4 :
(x-5) • (x-8)
Which is the desired factorization
Final result :<span> (x - 5) • (x - 8)
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