Factoring x2-45x+324
The first term is, x2 its coefficient is 1 .
The middle term is, -45x its coefficient is -45 .
The last term, "the constant", is +324
Step-1 : Multiply the coefficient of the first term by the constant 1 • 324 = 324
Step-2 : Find two factors of 324 whose sum equals the coefficient of the middle term, which is -45 .
-324 + -1 = -325 -162 + -2 = -164 -108 + -3 = -111 -81 + -4 = -85 -54 + -6 = -60 -36 + -9 = -45 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -36 and -9
x2 - 36x - 9x - 324
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-36)
Add up the last 2 terms, pulling out common factors :
9 • (x-36)
Step-5 : Add up the four terms of step 4 :
(x-9) • (x-36)
Which is the desired factorization
Equation at the end of step 1 :
(x - 9) • (x - 36) = 0
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