Middle term split of n(square)- 43n+463
Answers
Answer:
Step-by-step explanation:
n2+n-462=0
Two solutions were found :
n = 21
n = -22
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring n2+n-462
The first term is, n2 its coefficient is 1 .
The middle term is, +n its coefficient is 1 .
The last term, "the constant", is -462
Step-1 : Multiply the coefficient of the first term by the constant 1 • -462 = -462
Step-2 : Find two factors of -462 whose sum equals the coefficient of the middle term, which is 1 .
-462 + 1 = -461
-231 + 2 = -229
-154 + 3 = -151
-77 + 6 = -71
-66 + 7 = -59
-42 + 11 = -31
-33 + 14 = -19
-22 + 21 = -1
-21 + 22 = 1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -21 and 22
n2 - 21n + 22n - 462
Step-4 : Add up the first 2 terms, pulling out like factors :
n • (n-21)
Add up the last 2 terms, pulling out common factors :
22 • (n-21)
Step-5 : Add up the four terms of step 4 :
(n+22) • (n-21)
Which is the desired factorization
n2+n-462=0
Two solutions were found :
n = 21
n = -22
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring n2+n-462
The first term is, n2 its coefficient is 1 .
The middle term is, +n its coefficient is 1 .
The last term, "the constant", is -462
Step-1 : Multiply the coefficient of the first term by the constant 1 • -462 = -462
Step-2 : Find two factors of -462 whose sum equals the coefficient of the middle term, which is 1 .
-462 + 1 = -461
-231 + 2 = -229
-154 + 3 = -151
-77 + 6 = -71
-66 + 7 = -59
-42 + 11 = -31
-33 + 14 = -19
-22 + 21 = -1
-21 + 22 = 1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -21 and 22
n2 - 21n + 22n - 462
Step-4 : Add up the first 2 terms, pulling out like factors :
n • (n-21)
Add up the last 2 terms, pulling out common factors :
22 • (n-21)
Step-5 : Add up the four terms of step