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Factor 4n^2 - 5n -6​

User Pceccon
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1 Answer

4 votes

Answer:

(n-2) • (4n+3)

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)

User Jecjackal
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