Question

z square minus 12 Z + 27

Answer 1

Factoring z2-12z+27

The first term is, z2 its coefficient is 1 .
The middle term is, -12z its coefficient is -12 .
The last term, "the constant", is +27

Step-1 : Multiply the coefficient of the first term by the constant 1 • 27 = 27

Step-2 : Find two factors of 27 whose sum equals the coefficient of the middle term, which is -12 .

-27 + -1 = -28
-9 + -3 = -12 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and -3
z2 - 9z - 3z - 27

Step-4 : Add up the first 2 terms, pulling out like factors :
z • (z-9)
Add up the last 2 terms, pulling out common factors :
3 • (z-9)
Step-5 : Add up the four terms of step 4 :
(z-3) • (z-9)
Which is the desired factorization

Answer 2

z² - 12z + 27

By splitting the middle term method.

z² - 12x + 27

=> z² - 9z - 3x + 27

=> z(z - 9) - 3(x - 9)

=> (z - 9) (z - 3)


To factorise the above equation in the form of ax² + bx + c, find two numbers who sum is middle term and whose product is last term.