Perform the indicated operations. Write the resulting polynomial ...

Question

Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (-6x^3+7x^2-9x+3)+(14x^3+3x^2-11x-7)

Accepted Answer

Welcome back. I'm so glad you're here. We get to perform the indicated operation which is subtraction between these two bird polynomial is here. And so the first step is to carefully copy it. So nine X to the fifth minus four X. To the fourth plus five X to the third minus two X squared plus 0.99. And parentheses minus three X. To the fifth plus four X to the fourth minus. We get a fraction five thirds X squared minus 0.1. It's really important to copy that correctly because there's so many letters and numbers, it's easy to make a mistake. And the next part where it's really easy to make a mistake is um in failing to distribute this negative to all four of the terms in the second polynomial. So I write myself an extra step. That first term is going to become negative negative times a positive. Second term will become negative negative times a positive. The third term will become positive negative negative and the fourth term will become positive with a negative times a negative. So now we can drop the parentheses, we've distributed that negative and we can rewrite it nine X to the fifth minus four X. To the fourth plus five X to the third minus two X squared plus 0.99 minus three X to the fifth. And the second term is minus four X to the 4th. 3rd term is plus five thirds X squared and the last term is plus 0.1. Now it's just a matter of combining like terms. So our X to the fifth we got nine of them minus three of them is going to give us six X to the fifth. Now we've got our X to the force negative four and minus another four is going to give us negative eight X to the fourth. R X to the thirds. We've only got this one. This plus five X to the third. We bring that down now our X squared. Oh we've got our fraction. So we'll pause come up here and rewrite this negative two X squared plus five third X squared to add two terms where one's a fraction we want to have a common denominator to get the common denominator which will be three. We can multiply the negative two times. We want a three on the bottom so we put a three on the bottom and the top. So in effect we're multiplying it by one, multiplying across the top three times negative two is negative six and then multiplying across the bottom three times one is three. So we've got negative six thirds X squared plus five thirds X squared. And now we're adding so we can just look at the numerator negative six plus five. That's going to be negative one. So negative one in the denominator stays the same so negative one third X squared. That's how many X squares we have. So down here we say minus one third X squared. And now we're just looking at those regular terms because we don't have any X to the one. So .99 plus .01 is going to be plus one. Great. We have combined like terms and gotten that as simplified as possible. And now our next step is finding the degree of the polynomial to find the degree of the polynomial. We look at the degree of each term. And so we've got 545432 and zero. The highest terms degree is five, so the degree of the entire polynomial is five. And that leaves us with answer choice. A well done. You've done it have a good one. We'll catch you on the next one.

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