Question

unit 1 (exploring polynomial expressions through geometry) 1) when (4x⁵ + 11x⁴ - 6x² + 24) is added from (5x⁵ + 11x⁴ + 9x² - 25), what will be the result?

Explanation:

Step1: Set up the addition

We need to add the two polynomials \((4x^{5}+11x^{4}-6x^{2}+24)\) and \((5x^{5}+11x^{4}+9x^{2}-25)\). So we write the expression as \((4x^{5}+11x^{4}-6x^{2}+24)+(5x^{5}+11x^{4}+9x^{2}-25)\).

Step2: Combine like terms for \(x^{5}\)

The terms with \(x^{5}\) are \(4x^{5}\) and \(5x^{5}\). Combining them: \(4x^{5}+5x^{5}=(4 + 5)x^{5}=9x^{5}\).

Step3: Combine like terms for \(x^{4}\)

The terms with \(x^{4}\) are \(11x^{4}\) and \(11x^{4}\). Combining them: \(11x^{4}+11x^{4}=(11 + 11)x^{4}=22x^{4}\).

Step4: Combine like terms for \(x^{2}\)

The terms with \(x^{2}\) are \(-6x^{2}\) and \(9x^{2}\). Combining them: \(-6x^{2}+9x^{2}=(-6 + 9)x^{2}=3x^{2}\).

Step5: Combine constant terms

The constant terms are \(24\) and \(-25\). Combining them: \(24-25=-1\).

Step6: Write the final polynomial

Putting all the combined terms together, we get \(9x^{5}+22x^{4}+3x^{2}-1\).

Answer:

\(9x^{5}+22x^{4}+3x^{2}-1\)