Answer:
(x+6)⋅(x−9)
Step by Step
Factoring x2-3x-54
The first term is, x2 its coefficient is 1 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is -54
Step-1 : Multiply the coefficient of the first term by the constant 1 • -54 = -54
Step-2 : Find two factors of -54 whose sum equals the coefficient of the middle term, which is -3 .
-54 + 1 = -53
-27 + 2 = -25
-18 + 3 = -15
-9 + 6 = -3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 6
x2 - 9x + 6x - 54
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-9)
Add up the last 2 terms, pulling out common factors :
6 • (x-9)
Step-5 : Add up the four terms of step 4 :
(x+6) • (x-9)
Which is the desired factorization