Question

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

Answer 1

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)

Answer 2

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.