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Question
Find the remainder when p(x) = 3x2 + 2x – 7 is divided by 2x + 1.
Solution
Given a polynomial, p(x) = 3x2 + 2x – 7 ......(i)
Divisor, 2x + 1 = 0
⇒ x = `-1/2` ......(Put in (ii))
By the remainder theorem, we know that when p(x) is divided by x = ` 1/2`, the remainder is `p"(- 1/2)`.
∴ Putting x = `- 1/2` in the given polynomial, we get
`"P"(- 1/2) = 3(- 1/2)^2 + 2(- 1/2) - 7`
= `3(1/4) - 2(1/2) - 7`
= `3/4 - 1 - 7`
= `3/4 - 8`
= `- 29/4`
Hence, the remainder is `- 29/4`.
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