question\nfactor the trinomial:\n$2x^2 + 9x + 7$

Explanation:

Step1: Identify coefficients and constant

For trinomial (2x^2 + 9x + 7), (a = 2), (b = 9), (c = 7).

Step2: Find two numbers

Find two numbers that multiply to (a\times c=2\times7 = 14) and add to (b = 9). The numbers are (2) and (7) (since (2\times7 = 14) and (2 + 7=9)).

Step3: Split the middle term

Rewrite the middle term using these numbers: (2x^2+2x + 7x + 7).

Step4: Factor by grouping

Group the first two and last two terms: ((2x^2 + 2x)+(7x + 7)). Factor out common factors: (2x(x + 1)+7(x + 1)).

Step5: Factor out common binomial

Factor out ((x + 1)): ((2x + 7)(x + 1)).

Answer:

((2x + 7)(x + 1))