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For the function: 2x^4 -3x^3 + 2x-4, find the zeroes. Show all work

Mathematics
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Alright, good sir! Allow me to help! We need to factor this sucker, so hold on to your knickers. We have an x^4 an x^3 and an x^1 (or just x), so we need to factor using x^3 and x since we can make the x^4 through multiplication. We have the following equation: 2x^4 - 3x^3 + 2x -4 = 0 We set the equation equal to zero so we can find when it crosses the x axis (the zeroes). Now, we want to use our own numeral for the final number so let's move it over to the other side: 2x^4 - 3x^3 + 2x = 4 Lets try factoring this. Through some serious trial and error (not that hard, just see what you have to multiply to find this number) you can find the factors: (x^3 + __ )*(2x + __ ) = 4 + __ I got the 2 in front of the x because I knew we needed a 2x^4. Now, try it out and find what you need - here a 1 and -3 work: (x^3 + 1 )*(2x - 3 ) = 4 + __ Now we need to find that number on the other side of the equation, so multiply the two out: 2x^4 - 3x^3 +2x - 3 = 4 - 3 It ended up being -3. Fun Fun. Now lets go back to the factors and put that -3 in: (x^3 +1)*(2x - 3) = 1 Now, we need to make this equation work and the only way this will work is if both parts on the left equal 1: (x^3 +1) = 1 and (2x-3)=1 x^3=0 and 2x=4 x=0 and x=2 There you go! I really hope I didn't make a mistake anywhere o.o.
Wow thank you so much! I know that took a lot of time. I would give you 100 medals if I could!

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