Question

Find the remainder when p(x) = 3x² + 2x – 7 is divided by 2x + 1.

Answer 1

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`.