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Misha Larkins [42]
3 years ago
11

Please help me . factor. X^2-13x+40

Mathematics
2 answers:
Ainat [17]3 years ago
6 0
Consider the factors of 40: ±1, ±4, ±10, ±5, ±8 ... ±5 and <span>±8 can be manipulated to fit your factorization.

(x - 8)(x - 5) works. -8 - 5 = -13, which is what you need in the middle, and -8*-5 gives you a positive 40.</span>
zepelin [54]3 years ago
3 0

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)

</span>
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