Question

which expression is equivalent to $6n^2 + 19n - 20$
not factorable
$(n + 4)(6n - 5)$
$(n - 4)(6n + 5)$
$(n - 10)(9n - 10)$

Explanation:

Step1: Expand each option

For option B: \((n + 4)(6n - 5)\)
Using the distributive property (FOIL method):
First: \(n\times6n = 6n^2\)
Outer: \(n\times(-5)=-5n\)
Inner: \(4\times6n = 24n\)
Last: \(4\times(-5)=-20\)
Combine like terms: \(6n^2-5n + 24n-20=6n^2 + 19n-20\)
We can check other options to be sure.
For option C: \((n - 4)(6n + 5)\)
First: \(n\times6n = 6n^2\)
Outer: \(n\times5 = 5n\)
Inner: \(-4\times6n=-24n\)
Last: \(-4\times5=-20\)
Combine like terms: \(6n^2+5n-24n - 20=6n^2-19n-20\) (not equal)
For option D: \((n - 10)(9n - 10)\)
First: \(n\times9n = 9n^2\)
Outer: \(n\times(-10)=-10n\)
Inner: \(-10\times9n=-90n\)
Last: \(-10\times(-10) = 100\)
Combine like terms: \(9n^2-10n-90n + 100=9n^2-100n + 100\) (not equal)

Answer:

B. \((n + 4)(6n - 5)\)