sari is factoring the polynomial (2x^{2}+5x + 3). if one factor is ((x + 1)), what is the other…

Explanation:

Step1: Divide the polynomial by the known factor

We use polynomial long - division or the method of comparing coefficients. Let the other factor be (ax + b). Then ((x + 1)(ax + b)=ax^{2}+(a + b)x + b). We know that (ax^{2}+(a + b)x + b=2x^{2}+5x + 3). Comparing the coefficients of (x^{2}): (a = 2).

Step2: Compare the coefficients of (x) and the constant term

Since (a = 2), and comparing the coefficients of (x): (a + b=5). Substitute (a = 2) into (a + b=5), we get (2 + b=5), so (b = 3).

Answer:

B. (2x + 3)