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

3

Explanation:

The polynomial is:

(1)

We want to factorize it as follows:

where C is the unknown number we want to find.

Solving explicitely the last equation,

(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