AT&T; ii 84% a 9:24 PM finding zeros of a polynom... DETAILS SUBMISSIONS GRADE L

Question

AT&T; ii 84% a 9:24 PM finding zeros of a polynom... DETAILS SUBMISSIONS GRADE List the possible rational zeros for each problem using the rational zero theorem and then use synthetic division to find the actual zeros (solutions). If you get a remainder of zero while doing the synthetic division but cannot factor the answer, you do NOT have try to go further. Be sure to try the ac method of factoring before giving up on factoring. READ the finding zeros of a polynomial module before attempting this assignment. Once you submit your work, no other submissions will be accepted. f () 223 +7a2 -10x - 24 2 f (x)-2x3-3x2-32x-15 3. Dashboard

Explanation / Answer

1) f(x) = 2x^3 + 7x^2 - 10x - 24

rational zeros are

+- { 1 , 2 , 3 , 6 , 8, 12 , 24 } / { 1 , 2 }

+- { 1 , 1/2 , 2 , 2/2, 3 , 3/2 , 4 , 4/2 , 6 , 6/2 , 8 , 8/2 , 12 , 12 /2 , 24 , 24/2 }

one actual zero is at x - 2

dividing the polynomial by x -2

we get

2x^2 + 11x + 12

finding remaining zeros by ac method

( 2 x + 3 ) ( x + 4 ) = 0

x = -3/2 , x = -4

zeros of the polynomial are x = 2 , -3/2 , -4

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