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