Question

Sari is factoring the polynomial 2x2 + 5x + 3. What is the missing number in her factorization? 2x2 + 5x + 3 = (2x +[ ? ])(x + 1)

Answer 1

Answer: 3

Explanation:

The polynomial is:

$2x^2+5x+3$ (1)

We want to factorize it as follows:

$(2x+C)(x+1)$

where C is the unknown number we want to find.

Solving explicitely the last equation,

$(2x+C)(x+1)=2x^2 +2x +Cx +C=2x^2 +(2+C)x+C$ (2)

We want eq.(2) to be identical to eq.(1). From the last term, we see immediately that it must be C=3, and 2+C=5. So the missing number is 3, and the factorization is

$(2x+3)(x+1)$