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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 $a$ be a constant. What is the largest possible degree of $f(x) + a\cdot g(x)$?

 

3)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 $f(x) + b\cdot g(x)$?

 

4)Let $f(x) = x^4-3x^2 + 2$ and $g(x) = 2x^4 - 6x^2 + 2x -1$. What is the degree of $f(x) \cdot g(x)$?

 

5)Find $t$ if the expansion of the product of $x^3 - 4x^2 + 2x - 5$ and $x^2 + tx - 7$ has no $x^2$ term.

 

thanks :D 

off-topic
 Mar 23, 2019
edited by Android4EVER  Mar 23, 2019
edited by Android4EVER  Mar 23, 2019
 #1
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Hey Android4EVER,

The images that you insterted say "Waiting for Moderation" answerers can't see the diagrams and answer. 

You should try this:

 

 

If you "right click"  on the image and select  "Copy Image Address".....you can open up a new browser  window and paste this address into it......hit "Enter"  and you should be able to see the image

 

Hope this Helps :)

 Mar 23, 2019
 #2
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1)

All we have to do is add the coefficients of the x^3 terms, or 1 + 5 = 6.

 

2) 

Because a is a constant, the largest possible must be 4, as a cannot change the degree.

 

3)

We want to have the smallest possible degree, so we should cancel terms. So, we set b = -1/2 and the degree of the sum is 1.

 

4)

To find the degree of the porduct, we just add the degrees of the functions. So, our answer is 4 + 4 = 8.

 

5)

We can find which terms multiply to get something with x^2 in it. We get 28 + 2t - 5 = 0, or 23 + 2t = 0 => t = -11.5.

 

Hoping this helped,

asdf334

 Mar 23, 2019

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