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Chapter 0: Problem 9

Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. $$\left(-6 x^{3}+5 x^{2}-8 x+9\right)+\left(17 x^{3}+2 x^{2}-4 x-13\right)$$

Short Answer

Expert verified
The resulting polynomial in standard form is \( 11x^3 + 7x^2 -12x -4 \) and its degree is 3.

Step by step solution

01

Identify Like Terms

In both polynomials, the like terms are the ones that have the same variable and exponent. So, \( -6x^3 \) and \( 17x^3 \) are like terms, \( 5x^2 \) and \( 2x^2 \) are like terms, \( -8x \) and \( -4x \) are like terms and lastly, \( 9 \) and \( -13 \) are like terms.
02

Perform Addition of Like Terms

Now, add the coefficients of like terms: \((-6x^3 + 17x^3)\), \((5x^2 + 2x^2)\), \((-8x + -4x)\), and \((9 + -13)\). The resulting polynomial is \( 11x^3 + 7x^2 -12x -4 \).
03

Write Polynomial in Standard Form and Indicate Degree

The standard form of a polynomial arranges the terms by degree in descending order. Since the terms are already ordered from highest to lowest degree, the standard form is \( 11x^3 + 7x^2 -12x -4 \). The degree of the polynomial is the highest exponent in the polynomial and in our case, the highest exponent is 3. So, the degree of the polynomial is 3.

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