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प्रश्न
Show that (x − 2), (x + 3) and (x − 4) are factors of x3 − 3x2 − 10x + 24.
उत्तर
Let `f(x) = 2^3 - 3x^2 - 10x + 24` be the given polynomial.
By factor theorem,
(x-2) , (x+3)and (x-4) are the factor of f(x).
If f(2) , f(-3)and f(4) are all equal to zero.
Now,
`f(2) = (2)^3 - 3(2)^2 - 10(2) + 24`
`= 8 -12 - 20 +24`
`= 32 -32`
` = 0`
also
`f(-3) = (-3)^3 -3(-3)^2 - 10(-3) + 24`
` = -27 -27 + 30 + 24`
` = -54 + 54`
` = 0`
And
`f(4)= (4)^3 - 3(4)^2 - 10(4) + 24`
` = 64 - 48 - 40 + 24`
`= 88 - 88`
= 0
Hence, (x − 2), (x + 3) and (x-4) are the factor of polynomial f(x).
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