find the all of the zeros
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Sia ? 4 years, 9 months ago
Given polynomial is x4 + x3 - 34x2 - 4x + 120
Since, the two zeroes of the polynomial given is 2 and -2
So, factors are (x + 2)(x - 2) = x2 + 2x - 2x - 4 = x2 - 4
dividend = divisor × quotient + remainder
dividend= x4 + x3 - 34x2 - 4x + 120
divisor = x2 - 4
quotient = x2 + x - 30
remainder = 0
So, x4 + x3 - 34x2 - 4x + 120 = (x2 - 4)(x2 + x - 30)
= (x - 2)(x + 2)(x2 + 6x - 5x - 30)
= (x - 2)(x + 2)(x + 6)(x - 5)
Therefore, the zeroes of the polynomial = x = 2, -2, -6, 5
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