Find all the zeroes of x3-10x2+31x-30 if 2 is a zero of it
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Answer:
Hence the zeroes are 2, 3 and 5.
Explanation:
2 is a zero.
Therefore, (x-2) is a factor or x3-10x2+31x-30.
Then perform long division, divide x3-10x2+31x-30 by (x-2).
We get the quotient as:
x2-8x+15
= x2-5x-3x+15 (splitting the middle term)
= x(x-5) -3(x-5)
= (x-3)(x-5).
Therefore, factors of x3-10x2+31x-30 are (x-2), (x-3) and (x-5).
Hence the zeroes are 2, 3 and 5.
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