Question

What is the missing term in the factorization of 2x2 + 5x + 3?

(2x + 3)(x + )

Answer 1

(x + 1)

As:

(2x + 3)(x + 1) = 2x2 + 2x + 3x + 3

= 2x2 + 5x + 3

Answer 2

The missing term is
`1`

Explanation:

we have

`2x^(2) +5x+3`

Let

b-----> the missing term

we know that

`2x^(2) +5x+3=(2x+3)(x+b)`

solve for b

`2x^(2) +5x+3=(2x+3)(x+b)\\ \\2x^(2) +5x+3=2x^(2) +2xb+3x+3b\\ \\2x^(2) +5x+3=2x^(2) +x(2b+3)+3b`

Solve the system

`2b+3=5` ------>
`b=1`

Verify in the second equation

`3b=3` ------> substitute the value of b ---->
`3=3` --> is ok

therefore

`2x^(2) +5x+3=(2x+3)(x+1)`