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Home Q & A Board Science-Related Homework Help Mathematics
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moni_shorty@ moni_shorty@
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11 years ago
Factor the polynomial and use the factored form to find the zeros.


P(x)=1/12 (2x^4 + 3x^3 - 16x -24)^2

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#1
11 years ago
1/12 (2x^4 + 3x^3 - 16x -24)^2 = 0

2x^4 + 3x^3 - 16x - 24 = 0

x^3(2x + 3) - 8(2x + 3) = 0 {grouping}

(x^3 - 8)(2x + 3) = 0

(x - 2)(x^2 + 2x + 4)(2x + 3) = 0 {difference of two cubes}

x - 2 = 0
x = 2

x^2 + 2x + 4 = 0
x = [-2 +/- sqrt(4 - 16)]/2
x = [-2 +/- 2isqrt(3)]/2
x = -1 +/- isqrt(3)

2x + 3 = 0
2x = -3
x = -3/2
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