Factoring Quadratic Trinomials 6n^2 - n - 40 =

(3n - 8)(2n + 5)

Step-by-step explanation:

6n² - n - 40

Consider the factors of the product of the coefficient of the n² term and the constant term which sum to give the coefficient of the n- term

product = 6 × - 40 = - 240 and sum = - 1

The factors are - 16 and + 15

Use these factors to split the n- term

6n² - 16n + 15n - 40 ( factor the first/second and third/fourth terms )

2n(3n - 8) + 5(3n - 8) ← factor out (3n - 8) from each term

(3n - 8)(2n + 5)

Then

6n² - n - 40 = (3n - 8)(2n + 5)

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