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Use Remainder Theorem to Factorize the Following Polynomial: `2x^3 + 3x^2 - 9x - 10` - ICSE Class 10 - Mathematics

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Question

Use Remainder theorem to factorize the following polynomial:

`2x^3 + 3x^2 - 9x - 10`

Solution

Let P(x) = `2x^3 + 3x^2 - 9x - 10`

P(2) = 16 + 12 - 18 - 10

P(2) = 0

So (x - 2) is a factor

Let us divide P(x) with (x-2), we get

`(x- 2)(2x^2 + 7x + 5)`

This can be further factored to

`(x-2)(2x^2 + 5x + 2x + 5)` ……… (Split 7x into two terms, whose sum is 7x and product is10𝑥2)

`(x - 2) (2x^2 + 5x + 2x + 5)`

`(x - 2))(x(2x+5)+1(2x+5))`

(x - 2)(2x + 5)(x + 1)

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Solution Use Remainder Theorem to Factorize the Following Polynomial: `2x^3 + 3x^2 - 9x - 10` Concept: Remainder Theorem.
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