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F(X) = 4x3 − 12x2 + 14x − 3, G(X) 2x − 1 - Mathematics

Answer in Brief

f(x) = 4x3 − 12x2 + 14x − 3, g(x) 2x − 1

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Solution

Let us denote the given polynomials as

`f(x) = 4x^2 - 12x^3 - 12x^2 + 14x - 3,`

`g(x) = 2x - 1`

`⇒ g (x) = 2 (x - 1/2)`

We have to find the remainder when f(x) is divided by g(x).

By the remainder theorem, when f(x) is divided by g(x) the remainder is

`f(1/2) = 4(1/2)^3 - 12(1/2)^2 + 14 (1/2) - 3`

            ` = 4 xx 1/8 - 12  xx 1/4 + 14 xx 1/2 - 3`

            `  = 1/2 -3 + 7 - 3`

             `= 3/2`

Now we will calculate the remainder by actual division

So the remainder by actual division is `3/2` .

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 6 Factorisation of Polynomials
Exercise 6.3 | Q 4 | Page 14
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