Answer:
The missing term is [tex]1[/tex]
Step-by-step explanation:
we have
[tex]2x^{2} +5x+3[/tex]
Let
b-----> the missing term
we know that
[tex]2x^{2} +5x+3=(2x+3)(x+b)[/tex]
solve for b
[tex]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[/tex]
Solve the system
[tex]2b+3=5[/tex] ------>[tex]b=1[/tex]
Verify in the second equation
[tex]3b=3[/tex] ------> substitute the value of b ----> [tex]3=3[/tex] --> is ok
therefore
[tex]2x^{2} +5x+3=(2x+3)(x+1)[/tex]
