Question

x2-21x+108 factorise it

Answer 1

Factoring x2-21x+108

The first term is, x2 its coefficient is 1 .
The middle term is, -21x its coefficient is -21 .
The last term, "the constant", is +108

Step-1 : Multiply the coefficient of the first term by the constant 1 • 108 = 108

Step-2 : Find two factors of 108 whose sum equals the coefficient of the middle term, which is -21 .

-108 + -1 = -109
-54 + -2 = -56
-36 + -3 = -39
-27 + -4 = -31
-18 + -6 = -24
-12 + -9 = -21 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -9
x2 - 12x - 9x - 108

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-12)
Add up the last 2 terms, pulling out common factors :
9 • (x-12)
Step-5 : Add up the four terms of step 4 :
(x-9) • (x-12)

Answer 2

x^2-12x-9x+108
x(x-12)-9(x-12)
(x-12)(x-9)
x=12 or x=9