I just learned synthetic division today and I'm confused about the zeros. For example in the equation:
(5x^6 - 3x^5 + 2x - 7) divided by (x + 2)
I know there are three zeros when I divide it...BUT WHY?
Please help! D: WHAT are the zeros for?
2007-08-22 15:58:08 · 4 answers · asked by dk 3 in Science & Mathematics ➔ Mathematics
Ohhhhh... but how do I know where to place them?
2007-08-22 16:03:35 · update #1
The zeros are place markers for the terms which have no coefficient.
(x+2)/ 5x^6 - 3x^5 + 0x^4 + 0x^3 + 0x^2 +2x - 7
The zeros are so once you begin diving you wont forget to carry the remainder to the proper coefficient of x. I hope this is what confused you and makes more sense now.
2007-08-22 16:08:03 · answer #1 · answered by revolutionist1985 2 · 0⤊ 0⤋
Because you need to account for the x^4, x^3, x^2 place. The zeroes are place holders. 1st set it up: (x+2)division sign (5x^6-3x^5+0x^4+0x^3+0x^2+2x-7. Then work on the x's: on top of the x^6 place put 5x^5 because that is what is needed to make 5x^6. Under 5x^6: put your 5x^6+10x^5 which is what you get by multiplying 5x^5 by (x-2). Then change the signs to subtract you will get (-13x^5) after subtracting. Then on top of the -3x^5, put a (-13x^4) and repeat the steps. Your final answer should be 5x^5-13x^4+26x^3-52x^2+104x-206+405 if I didn't make a mistake. I hope it helps, just don't forget to change the signs and learn the steps and you will be fine.
2007-08-22 23:02:49 · answer #2 · answered by David G 3 · 0⤊ 0⤋
well, the actual equation is 5x^6 - 3x^4 + 0x^4 + 0x^3 + 0x^2 + 2x - 7, people just dont usually say the 0's, but you dont want to forget them in synthetic.
2007-08-22 23:05:13 · answer #3 · answered by climberguy12 7 · 0⤊ 0⤋
the zeros are to take the place of the x^4 and x^3 and x^2 that are missing from the original equation.
2007-08-22 23:01:56 · answer #4 · answered by sophia 3 · 0⤊ 0⤋