Question

what is the sum of the polynomials ((1/4)x^2 - 3x + 2.25)+(0.75x^2 + 2x - 1/4)

Answer 1

To find the sum of the given polynomials \(\left(\frac{1}{4}x^2 - 3x + 2.25\right) + \left(0.75x^2 + 2x - \frac{1}{4}\right)\), we will combine like terms.

First, let's rewrite the constants in the second polynomial:

\[
0.75x^2 = \frac{3}{4}x^2,
\]
and
\[
- \frac{1}{4} = -0.25.
\]

Now we can write it as:

\[
\left(\frac{1}{4}x^2 - 3x + 2.25\right) + \left(\frac{3}{4}x^2 + 2x - 0.25\right).
\]

Now we can combine the like terms:

1. **Combining the \(x^2\) terms:**
\[
\frac{1}{4}x^2 + \frac{3}{4}x^2 = \left(\frac{1}{4} + \frac{3}{4}\right)x^2 = \frac{4}{4}x^2 = 1x^2.
\]

2. **Combining the \(x\) terms:**
\[
-3x + 2x = (-3 + 2)x = -1x = -x.
\]

3. **Combining the constant terms:**
\[
2.25 - 0.25 = 2.00 = 2.
\]

Now combining all the results:

\[
1x^2 - x + 2.
\]

Thus, the sum of the polynomials is:

\[
\boxed{x^2 - x + 2}.
\]