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# halp with functions :)

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1)Let $$f(x) = x^3 + 3x ^2 + 4x - 7$$ and $$g(x) = -7x^4 + 5x^3 +x^2 - 7$$. What is the coefficient of $$x^3$$ in the sum $$f(x) + g(x)$$?

2) Let $$f(x) = x^4-3x^2 + 2$$ and $$g(x) = 2x^4 - 6x^2 + 2x -1$$. Let b be a constant. What is the smallest possible degree of the polynomial $$f(x) + b\cdot g(x)?$$

also if you could explane what degree means in functions that would be great too :)

Any help will be great.

THX IN ADVANCE $$:)$$

srry for all the changes.

Aug 21, 2019
edited by Guest  Aug 21, 2019
edited by Guest  Aug 21, 2019
edited by Guest  Aug 21, 2019

#1
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$$1) ~1 + 5 = 6\\~\\ 2)~\text{The degree of a polynomial f(x) is its highest power of x \\f(x)+bg(x) will be of degree 4}$$

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Aug 21, 2019
#2
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Answer 1 was correct but 2 was not. thx for question 1 tho !!

Aug 21, 2019
#3
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(2)   If we let  b  = -1/2  we have

f(x)  + (-1/2) g(x)   =

x^4 -3x^2 + 2  +  - (1/2) [2x^4 - 6x^2 + 2x - 1 ]  =

x^4 - 3x^2 + 2  - x^4 - 3x^2 - x + 1/2  =

-x + 2 + 1/2  =

-x + 5/2   ⇒   degree  1   is the smallest possible degree

Aug 21, 2019
#4
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Thx CPhill The answer was correct

Guest Aug 21, 2019
#6
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I belive that the motivation for substituting $$b=-\frac 12$$ was to cancel out the $$2x^4$$ term. Then, you easily work your way to the correct answer.

Aug 22, 2019