question\nfactor the trinomial:\n5x² + 17x + 14

Explanation:

Step1: Multiply the coefficient of (x^{2}) and the constant term

For the trinomial (5x^{2}+17x + 14), (a = 5), (b=17), (c = 14). Calculate (a\times c=5\times14 = 70).

Step2: Find two numbers that multiply to (70) and add up to (17)

The numbers are (7) and (10) since (7\times10=70) and (7 + 10=17).

Step3: Rewrite the middle term

Rewrite (17x) as (7x+10x). So, (5x^{2}+17x + 14=5x^{2}+7x+10x + 14).

Step4: Group the terms

Group the terms as ((5x^{2}+7x)+(10x + 14)).

Step5: Factor out the common factors from each group

From (5x^{2}+7x), factor out (x) to get (x(5x + 7)). From (10x + 14), factor out (2) to get (2(5x + 7)).

Step6: Factor out the common binomial factor

Now, (x(5x + 7)+2(5x + 7)=(5x + 7)(x + 2)).

Answer:

((5x + 7)(x + 2))