factorise by splitting the middle term x2+21x+108
Answers
Answer:
, (x - 9) • (x - 12)
Step-by-step explanation:
Step 1 :
Trying to factor by splitting the middle term
1.1 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)
Which is the desired factorization
Answer:
=x2-12x-9x+108
=x(x-12)-9(x-12)
=(x-9)(x-12)
Hope this is helpful..