Factorize x2 – 24x+144 by splitting middle term.
Answers
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
STEP 1:
Trying to factor by splitting the middle term
1.1 Factoring x2-24x+144
The first term is, x2 its coefficient is 1 .
The middle term is, -24x its coefficient is -24 .
The last term, "the constant", is +144
Step-1 :
Multiply the coefficient of the first term by the constant 1 • 144 = 144
Step-2 :
Find two factors of 144 whose sum equals the coefficient of the middle term, which is -24 .
-144 + -1 = -145
-72 + -2 = -74
-48 + -3 = -51
-36 + -4 = -40
-24 + -6 = -30
-18 + -8 = -26
-16 + -9 = -25
-12 + -12 = -24 That's it
Step-3 :
Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -12
x2 - 12x - 12x - 144
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 :
12 • (x-12)
Step-5 :
Add up the four terms of step 4 :
(x-12) • (x-12)
Which is the desired factorization
Multiplying Exponential Expressions:
1.2 Multiply (x-12) by (x-12)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x-12) and the exponents are :
1 , as (x-12) is the same number as (x-12)1
and 1 , as (x-12) is the same number as (x-12)1
The product is therefore, (x-12)(1+1) = (x-12)2
Final result :
(x - 12)2
Answer:
x2 -24x+144=0
x2-12x-12x+144=0
x[x-12] -12[x-12]=0
[x-12] [x-12] =0
x=12
Step-by-step explanation: