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Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:(i) `p(x)=2x^3+x^2-2x-1,g(x)=x+1`
(ii) `p(x)=x^3+3x^2+3x+1,g(x)=x+2`
(iii) `p(x)=x^3+4x^2+x+6,g(x)=x-3`

Text Solution

Verified by Experts

From Factor theorem,
`(y-a)` is a factor of `P(y) if P(a) = 0.`

(i)`p(x) = 2x^3+x^2-2x-1 and g(x) = x+1`
For `g(x)` to be a factor of `p(x)`, `p(-1)` should be `0`.
`p(-1) = 2(-1)^3+(-1)^2-2(-1) -1 `
`=-2+1+2-1 =0` As, `p(-1)` is `0`, `(x+1)` is a factor of `p(x)`.

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