Divide.

16x^4−24x^3+3 / 4x^2+3
fill in the boxes(spaces lol)
= x^2 - x - + /

Enter your answer by filling in the boxes.

Question

Divide.

16x^4−24x^3+3 / 4x^2+3
fill in the boxes(spaces lol) 
=      x^2  -    x  -      +         /

Enter your answer by filling in the boxes.

summerh0819 · Answer

attachment

TogaHimiko · Answer

u need help on tht one also?

TogaHimiko · Answer

ohhh ok

summerh0819 · Answer

no thats the question i just snipped a picture of it so you could see it

TogaHimiko · Answer

k

FexrlessRxby · Answer

So do you know what to do to start off?

SmokeyBrown · Answer

We can use the method described in this screenshot (taken from the website: https://byjus.com/maths/polynomial-division/ ) 4x^2 + 3 INTO 16x^4−24x^3 + 0x^2 + 0x +3 Let's start with the "leading terms" as the method describes: 4x^2 can be multiplied by 4x^2 to go into 16x^4. So, let's multiply the entire expression (4x^2 + 3) by 4x^2, giving us (16x^4 + 12x^2) We then subtract this from the dividend so that our new expression is: 4x^2 + 3 INTO 24x^3 - 12x^2 + 0x +3 (and our quotient so far is 4x^2...) We'll continue using leading terms: 4x^2 can be multiplied by 6x to go into 24x^3. Once again, we multiply the entire expression (4x^2 + 3) by 6x to get (24x^2 + 18x) and subtract this from the dividend to get: 4x^2 + 3 INTO -12x^2 -18x + 3 (our quotient so far is 4x^2 + 6x...) Just like before, 4x^2 can be multiplied by -3 to go into -12x^2, so we multiply (4x^2 + 3) by -3 to get (-12x^2 - 9), subtract it from the dividend to get: 4x^2 + 3 INTO -18x + 12 (our quotient so far is 4x^2 + 6x - 3) Now, 4x^2 does not go into -18x, so our long-division ends here. The quotient we find through this method of polynomial long-division is (4x^2 + 6x - 3) and the remainder is (-18x + 12) Perhaps you can use these results to fill in the blanks of your question? I hope this helps with your understanding of the concept; please let me know if there's any further guidance I can give :)

AZ · Answer

I think both of you might want to check your work again $\dfrac{16 x^4 - 24 x^3 + 3}{4x^2+3} = 4x^2 - 6 x - 3 + \dfrac{18 x + 12}{4x^2+3} $ https://www.wolframalpha.com/input/?i=%2816x%5E4%E2%88%9224x%5E3%2B3+%29%2F+%284x%5E2%2B3%29

SmokeyBrown · Answer

@az wrote:

I think both of you might want to check your work again $\dfrac{16 x^4 - 24 x^3 + 3}{4x^2+3} = 4x^2 - 6 x - 3 + \dfrac{18 x + 12}{4x^2+3} $ https://www.wolframalpha.com/input/?i=%2816x%5E4%E2%88%9224x%5E3%2B3+%29%2F+%284x%5E2%2B3%29

Indeed. How odd. I wonder what I did wrong to get the result I got? Well, anyway, thanks for double-checking and providing the correct solution!

surjithayer · Answer

i am sorry ,i will do it again
4x^2+3)16x^4-24x^3+0x^2+0x+3(4x^2-6x-3

16x^2           +12x^2
             -                     -
             ______________________
                        -24x^3-12x^2 + 0x
                       -24x^3              -18x
                       +                       +
                     ______________________________
                                    -12x^2+18x+3
                                    -12 x^2        -9
                                    +                  +
                                   _________________
                                                   18x+12
                                                ____________
$$\frac{ 16x^4-24x^3+3 }{ 4x^2+3 }=4x^2-6x-3+\frac{ 18x+12 }{ 4x^2+3}$$

AZ · Answer

@smokeybrown wrote:

Indeed. How odd. I wonder what I did wrong to get the result I got? Well, anyway, thanks for double-checking and providing the correct solution!

You went wrong with the signs `4x^2 can be multiplied by 6x to go into 24x^3` That is correct, but remember the original equation is 16x^4−24x^3+3 Since it's -24x that means, you need to multiply 4x^2 by -6x so that you can get -24x^2 so that when you subtract, it will cancel out -24x^2 - (-24x^2) = 0 It gets messy with the + and - signs when you write it out in text and Surjithayer's revised answer makes it easier to see to avoid that :)

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