Question 1040600: I am not understanding the long division of these if someone could please help. I have included what is expected.
Use the following polynomial functions to sketch the end behavior of the graph, state the zeros for the functions and the multiplicity of each zero, and determine the symmetry of each function.
f(x) = 2x3 + 3x2 – 8x – 12
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! f(x) = 2x3 + 3x2 – 8x – 12
The end behavior is to -oo for x going to minus infinity and +oo for x going to plus infinity.
The roots can be +/- factors of 12/+/- factors of 2.
1 does not work
try 2 with synthetic division:
2/2=======3=========-8=======-12
==2=======7=========6========12, which is 0. With synthetic division, bring down the first coefficient unchanged. Multiply it by the root (the divisor) and add it to the second term. Remember that the function must have placeholder 0 if something (x or x^2) is missing. 2*2 is 4, and that is added to 3 to get 7. Then multiply that by 2 to get 14, which when added to -8 gives 6. Multiply that by 2 which gives +12 and that added to -12 is 0. Therefore, 2 is a root, and (x-2) is a factor. What is left over is the new polynomial, one degree less than the first one.
(x-2) is a root, and the polynomial remaining is 2x^2+7x+6.
That factors into (2x+3)(x+2).
The roots are 2,-3/2.-2.
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