Factor 4n^2 - 5n - 6

(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)