What is the middle term?
Answers
Answer:
Step-by-step explanation:
7.2 Factoring n2 + 201n - 5400
The first term is, n2 its coefficient is 1 .
The middle term is, +201n its coefficient is 201 .
The last term, "the constant", is -5400
Step-1 : Multiply the coefficient of the first term by the constant 1 • -5400 = -5400
Step-2 : Find two factors of -5400 whose sum equals the coefficient of the middle term, which is 201 .
-5400 + 1 = -5399
-2700 + 2 = -2698
-1800 + 3 = -1797
-1350 + 4 = -1346
-1080 + 5 = -1075
-900 + 6 = -894
-675 + 8 = -667
-600 + 9 = -591
-540 + 10 = -530
-450 + 12 = -438
-360 + 15 = -345
-300 + 18 = -282
-270 + 20 = -250
-225 + 24 = -201
-216 + 25 = -191
-200 + 27 = -173
-180 + 30 = -150
-150 + 36 = -114
-135 + 40 = -95
-120 + 45 = -75
-108 + 50 = -58
-100 + 54 = -46
-90 + 60 = -30
-75 + 72 = -3
-72 + 75 = 3
-60 + 90 = 30
-54 + 100 = 46
-50 + 108 = 58
-45 + 120 = 75
-40 + 135 = 95
-36 + 150 = 114
-30 + 180 = 150
-27 + 200 = 173
-25 + 216 = 191
-24 + 225 = 201 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -24 and 225
n2 - 24n + 225n - 5400
Step-4 : Add up the first 2 terms, pulling out like factors :
n • (n-24)
Add up the last 2 terms, pulling out common factors :
225 • (n-24)
Step-5 : Add up the four terms of step 4 :
(n+225) • (n-24)
Which is the desired factorization
Equation at the end of step 7 :
3 • (n + 225) • (n - 24)
———————————————————————— = 0
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