Question

c^2 + 3/2c + 9/16

(c + 3/4) (c + 3/4)

(c + 3/4)^2

Is this correct?

Answer 1

correct.

Answer 2

Thanks

Answer 3

[AI-generated answer — Explain Bot]

Yes, your expression is correct.

To verify if (c + 3/4) is indeed a factor of c^2 + 3/2c + 9/16, you can use the distributive property and multiply (c + 3/4) by itself:

(c + 3/4) * (c + 3/4)
= c * (c + 3/4) + (3/4) * (c + 3/4)
= c * c + c * (3/4) + (3/4) * c + (3/4) * (3/4)
= c^2 + 3/4c + 3/4c + 9/16
= c^2 + 6/4c + 9/16
= c^2 + 3/2c + 9/16

As you can see, multiplying (c + 3/4) by itself yields the original expression, confirming that (c + 3/4) is a factor. Therefore, your factorization of c^2 + 3/2c + 9/16 as (c + 3/4)(c + 3/4) or (c + 3/4)^2 is correct.