The mistake that Danielle made is from the final equation of the polynomial. She did not write the degree of polynomial correctly. It should be 6x⁶ +2x²+ 2x - 8.
<h3>What is polynomial?</h3>
A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
To determine the sum of x³ + 5x²-7 and 5x³ - 3x² + 2x - 1
Danielle's Work :
(x³ + 5x² - 7) + (5x³ - 3x² + 2x - 1)
x³ + 5x³ + 5x² - 3x² + 2x - 7 - 1
6x⁶ +2x⁴ + 2x - 8
She did not write the degree of polynomial correctly
Correct Work :
(x³ + 5x² - 7) + (5x³ - 3x² + 2x - 1)
we have to open the brackets above
x³ + 5x² - 7 + 5x³ - 3x² + 2x - 1
x³ + 5x³ + 5x² - 3x² + 2x - 7 - 1
6x⁶ +2x²+ 2x - 8
Note that Danielle made the error in this step: 6x⁶ +2x⁴ + 2x - 8
The solution for the above is -2x² and not 2x⁴ as she wrote in her final equation.
Hence, the correct polynomial would be 6x⁶ +2x²+ 2x - 8
Learn more about polynomial here:
brainly.com/question/11536910
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