Question

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

Answer 1

Answer:

The missing term is $1$

Step-by-step 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

$2x^{2} +5x+3=(2x+3)(x+1)$

Answer 2

(x + 1)

As:

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

= 2x2 + 5x + 3