Step 1

To Determine: Factor the polynomial. If the polynomial cannot be factored state that it is prime.

Given:we have a polynomial \(12n^{2}+7n-10\)

Explanation: we have to find such number like on multiplying we get middle term and an adding or subtracting

we get 120.

\(a+or-b=7\)

\(a\times b=12\times 10=120\)

so we have

\(15-8=7\)

\(15\times 8 =120\)

we can writ down the polynomial as follows

\(12n^{2}-8n+15n-10\)

Step 2

Now taking common and solving we get

\((12n^{2}-8n)+(15n-10)\)

\(4n(3n-2)+5(3n-10)\)

\((4n+5)(3n-10)\)

so we have two factors.