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Find the remainder when f (x) = 12x^3 -...

Find the remainder when `f (x) = 12x^3 -13x^2 -5x +7` is divided by `(3x+2)`.

Text Solution

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`f(x) = 12x^3 -13x^2 - 5x + 7`
`3x+ 2 = 0`
`x = -2/3`
now as `f(x) = p(g(x)) + R`
`f(-2/3) = p(g(-2/3)) + R`
`f(-2/3) = R`
`R= 12(-2/3)^3 - 13(-2/3)^2 - 5(-2/3) + 7`
`= 12*(-8/27) - 13*4/9 + 10/3 + 7`
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