Question

find the difference. (2x + 3) - (2x² - x + 1) -2x² + ?x + \square

Explanation:

Step1: Distribute the negative sign

To subtract the polynomial \(2x^2 - x + 1\) from \(2x + 3\), we distribute the negative sign to each term in the second polynomial:
\[
(2x + 3) - (2x^2 - x + 1) = 2x + 3 - 2x^2 + x - 1
\]

Step2: Combine like terms

First, combine the \(x\)-terms: \(2x + x = 3x\).
Then, combine the constant terms: \(3 - 1 = 2\).
And the \(x^2\)-term remains \(-2x^2\).
Putting it all together, we get:
\[
-2x^2 + 3x + 2
\]

Answer:

The coefficient of \(x\) is \(3\) and the constant term is \(2\). So the filled-in expression is \(-2x^2 + \boldsymbol{3}x + \boldsymbol{2}\).