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Mathematics
Fisher Bridges
26 August, 22:13
Factor 4n^2 - 5n - 6
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Lance Orozco
26 August, 23:40
0
(n-2) • (4n+3)
Step-by-step explanation:
4n2-5n-6
Final result:
(n - 2) • (4n + 3)
Step by step solution:
Step 1:
Equation at the end of step 1:
(22n2 - 5n) - 6
Step 2:
Trying to factor by splitting the middle term
2.1 Factoring 4n2-5n-6
The first term is, 4n2 its coefficient is 4.
The middle term is, - 5n its coefficient is - 5.
The last term, "the constant", is - 6
Step-1 : Multiply the coefficient of the first term by the constant 4 • - 6 = - 24
Step-2 : Find two factors of - 24 whose sum equals the coefficient of the middle term, which is - 5.
-24 + 1 = - 23
-12 + 2 = - 10
-8 + 3 = - 5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 8 and 3
4n2 - 8n + 3n - 6
Step-4 : Add up the first 2 terms, pulling out like factors:
4n • (n-2)
Add up the last 2 terms, pulling out common factors:
3 • (n-2)
Step-5 : Add up the four terms of step 4:
(4n+3) • (n-2)
Which is the desired factorization
Final result:
(n - 2) • (4n + 3)
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