Question

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

Answer 1

Consider the factors of 40: ±1, ±4, ±10, ±5, ±8 ... ±5 and ±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.

Answer 2

Factoring  x2-13x+40 

The first term is,  x2  its coefficient is  1 .
The middle term is,  -13x  its coefficient is  -13 .
The last term, "the constant", is  +40 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 40 = 40 

Step-2 : Find two factors of  40  whose sum equals the coefficient of the middle term, which is   -13 .

     -40   +   -1   =   -41     -20   +   -2   =   -22     -10   +   -4   =   -14     -8   +   -5   =   -13   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  -5 
                     x2 - 8x - 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 : (x - 5) • (x - 8)