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Question
Show that 3x + 2 is a factor of 3x2 – x – 2.
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Solution
(x – a) is a factor of a polynomial f(x) if the remainder, when f(x) is divided by (x – a), is 0, i.e., if f(a) = 0.
f(x) = 3x2 – x – 2
`f((-2)/3) = 3((-2)/3)^2 - ((-2)/3) - 2`
= `3 xx 4/9 + 2/3 - 2`
= `4/3 + 2/3 - 2`
= `6/3 - 2`
= 2 – 2
= 0
Hence, 3x + 2 is a factor of 3x2 – x – 2
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