Write this trinomial in factored form.

3s^{2} + 10s + 7

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We will split the middle term to express the trinomial in factored form.

We have to find 2 numbers so that their product will equal

3*7=21(which is the product of coefficient of s^2 term and the constant term)

and also their sum will equal 10(which is the coefficient of v term).

Factors of 21 are

-1, -3, -7, -21, 1, 3, 7, 21

Selecting the 2 numbers from factors of 21 whose sum will equal 10, we get

3 and 7

(because 3*7=21 and 3+7=10)

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