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Chapter 0: Problem 10

Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. $$\left(-7 x^{3}+6 x^{2}-11 x+13\right)+\left(19 x^{3}-11 x^{2}+7 x-17\right)$$

Short Answer

Expert verified
The resulting polynomial in standard form is \(12x^{3} - 5x^{2} - 4x - 4\) and its degree is 3.

Step by step solution

01

Distribute the Sign

First distribute the positive sign into the second polynomial. This will not change the polynomial, but it's an important step to remember. The equation now is: \(-7x^{3} + 6x^{2} - 11x + 13 + 19x^{3} - 11x^{2} + 7x - 17\).
02

Group Like Terms

The goal is to group like terms together, which means identifying the terms with the same variable and degree. That that results in: \(-7x^{3} + 19x^{3} + 6x^{2} - 11x^{2} - 11x + 7x + 13 - 17\).
03

Simplify

Now, add and subtract those like terms: \ \[-7x^{3} + 19x^{3} = 12x^{3}\] \[6x^{2} - 11x^{2} = -5x^{2}\] \[-11x + 7x = -4x\] \[13 - 17 = -4\] Combining these results in: \(12x^{3} - 5x^{2} - 4x - 4\)
04

Determine the Degree

Finally, determine the degree of the polynomial. The degree of a polynomial is the highest power of the term with the highest degree. In this case, the degree is 3, from the term \(12x^{3}\)

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Most popular questions from this chapter

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