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Question
Show that (x – 2) is a factor of 3x2 – x – 10 Hence factorise 3x2 – x – 10.
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Solution
Let x – 2 = 0, then x = 2
Substituting the value of x in f(x),
f(x) = 3x2 – x – 10
= 3(2)2 – 2 – 10
= 12 – 2 – 10
= 0
∵ Remainder is zero
∴ x – 2 is a factor of f(x)
Dividing 3x2 – x – 10 by x – 2, we get
`x - 2")"overline(3x^2 - x - 10)("3x + 5`
3x2 – 6x
– +
5x – 10
5x – 10
– +
x
∴ 3x2 – x – 10 = (x – 2)(3x + 5).
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