Answer:
[tex](2x + 1)(x + 2)[/tex]
Step-by-step explanation:
To represent the algebraic expression [tex]2x^2 + 5x + 2[/tex] using algebraic tiles in a rectangular form, we need to factor it.
The expression [tex]2x^2 + 5x + 2[/tex] can be factored as follows:
Doing middle term factorization:
[tex] 2x^2 +(4+1)x + 2 [/tex]
[tex]2x^2 + 4x + x + 2[/tex]
[tex]2x(x + 2) + 1(x + 2)[/tex]
Now, we have a common factor of [tex]x + 2[/tex], so we can factor it out:
[tex](2x + 1)(x + 2)[/tex]
This representation shows a rectangular form with a length of [tex]2x + 1[/tex] and a width of [tex]x + 2[/tex].