Please show all work that leads up to the answer, also showthe unsimplified answ

Question

Please show all work that leads up to the answer, also showthe unsimplified answer too. Find a polynomial of degree 3 with constant coefficient 12 andzeros -1/2, 2 and 3. Ans: 4x3-18x2 + 14x +12 Other sinilar one: Fina polynomial of degree 4 having intergercoefficients and zeros 3i and 4, with 4 a double zero. Ans: NA Please show all work that leads up to the answer, also showthe unsimplified answer too. Find a polynomial of degree 3 with constant coefficient 12 andzeros -1/2, 2 and 3. Ans: 4x3-18x2 + 14x +12 Other sinilar one: Fina polynomial of degree 4 having intergercoefficients and zeros 3i and 4, with 4 a double zero. Ans: NA

Explanation / Answer

since the zeros are -1/2, 2 and 3 we know that x= -1/2, x=2 x=3 therefore: (x+1/2)(x-2)(x-3)=0 get rid of the fraction 1/2 by multiplying both sides of theequation by 2 and getting (2x+1)(x-2)(x-3)=0 foil (2x+1) and (x-2) 2x*x-2x*2+1*x-1*2   getting 2x2-4x+x-2 or 2x2 -3x-2 now we have (2x2 -3x-2)(x-3) now multiply this out x(2x2 -3x-2)-3(2x2 -3x-2) = 2x3 -3x2-2x-6x2 +9x+6 combine like terms to get 2x3 -9x2+7x+6 = 0 since the question says the constant has to be 12, multiply throughby 12/6 or 2 2*(2x3 -9x2+7x+6) = 0 *2 4x3 - 18x2 + 14x + 12 = 0

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