In Exercises 9–14, perform the indicated operations. Write the re...

Question

In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (−6x^3+5x^2−8x+9)+(17x^3+2x^2−4x−13)

Accepted Answer

Hi there. So this problem says the right to give them polynomial in standard forum after applying the stated operations. Also find the degree. So I'm gonna go ahead and rewrite this fall. No meals first we have eight X to the fourth minus three X squared plus three subtracted by negative X to the fourth plus three X squared plus two. So we want to subtract these two polynomial. So we're gonna combine like terms. But to do that I first need to deal with this minus in the middle. So I'm going to distribute this minus to everything to the right of it first this is gonna help us get rid of the negative and our parentheses. So distribute our minus. We have a negative a negative one would be in front of this sleeve. The one off for now we have negative Times Native X to the 4th then we have negative one times three X squared And a 91 times two summit. Go ahead and rewrite it again where we have eight X to the fourth minus three X squared plus three. That just comes directly down because we're not modifying it. Anyway. Now over here we have a negative one times a negative X. To the fourth. That will just turn it positive. It's the fourth. Do we have a negative one times a negative three to positive three X squared. Weather That turns into a -3 X square. We have a negative one times a positive to that just turns into negative too. Now we can go ahead and combine our like terms. So we have an X. To the fourth and we have an X. To the fourth. We can add those drugs together to get nine X. To the fourth. We also have a negative three X squared and another negative three X squared. Buying those together. We have negative three minus three. That is negative six X squared. Finally We have a positive three and -2, -2. Just turns into a positive one. So the equation is nine X. Fourth minus six X squared plus one. Now he's with the degree of the polynomial. The degree of the polynomial is just a degree of the highest exponent in the polynomial. So if you look here our degree, the highest exponent is four. So a degree is going to be equal to four. Thing that our answer is the equation nine to the fourth minus six X squared plus one With a degree of four. Making this answer. C. Okay I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (−6x^3+5x^2−8x+9)+(17x^3+2x^2−4x−13)

Key Concepts

Polynomial Addition

Standard Form of a Polynomial

Degree of a Polynomial

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