Question
\begin{tabular}{l} Add the following polynomials. Simplify your answer. \\ \( \qquad\left(-x^{2}-3 x+5\right)+\left(2-3 x+3 x^{2}+3 x^{3}\right) \) \\ Provide your answer below: \\ ( \\ \hline\end{tabular}
Ask by French Ayala. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The sum of the polynomials is \(3x^{3} + 2x^{2} - 6x + 7\).
Solution
Calculate or simplify the expression \( (-x^2-3x+5)+(2-3x+3x^2+3x^3) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(-x^{2}-3x+5\right)+\left(2-3x+3x^{2}+3x^{3}\right)\)
- step1: Remove the parentheses:
\(-x^{2}-3x+5+2-3x+3x^{2}+3x^{3}\)
- step2: Add the terms:
\(2x^{2}-6x+7+3x^{3}\)
The sum of the given polynomials is \(2x^{2}-6x+7+3x^{3}\).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To add the given polynomials, we will combine like terms. Starting with the expression: \[ (-x^2 - 3x + 5) + (2 - 3x + 3x^2 + 3x^3) \] First, rearrange and group the terms: \[ 3x^3 + (-x^2 + 3x^2) + (-3x - 3x) + (5 + 2) \] Now combine the coefficients of like terms: - For \(x^3\): \(3x^3\) - For \(x^2\): \(-x^2 + 3x^2 = 2x^2\) - For \(x\): \(-3x - 3x = -6x\) - For the constant terms: \(5 + 2 = 7\) Putting it all together, the simplified polynomial is: \[ 3x^3 + 2x^2 - 6x + 7 \] So the answer is: \[ 3x^3 + 2x^2 - 6x + 7 \]
