Question

Written as a simplified polynomial in standard form, what is the result when

(x + 2)2 is subtracted from 8x + 9?

Answer 1

To find the result of subtracting (x + 2)^2 from 8x + 9, we first expand (x + 2)^2, then subtract the resulting x^2 + 4x + 4 from 8x + 9, and simplify to get the final answer, which is the polynomial -x^2 + 4x + 5.

Step-by-step explanation:

To find the result of subtracting (x + 2)^2 from 8x + 9, we need to first expand (x + 2)^2:

(x + 2)^2 = x^2 + 4x + 4

Now, we subtract this expression from 8x + 9:

8x + 9 - (x^2 + 4x + 4)

This simplifies to:

8x + 9 - x^2 - 4x - 4

We combine like terms:

-x^2 + 8x - 4x + 9 - 4

Which results in:

-x^2 + 4x + 5

Therefore, the simplified polynomial in standard form is -x^2 + 4x + 5.