Question

question
factor the trinomial:
$2x^2 + 9x + 7$

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:

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