What should be subtracted from $3 x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 3$ , so that the resulting polynomial is exactly divisible by $(3 x + 2)$ ?

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- \frac{185}{27}

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\frac{185}{27}

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None of these

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Solution

The correct option is C $\frac{185}{27}$

To get the polynomial that is exactly divisible by $g (x) = 3 x + 2$ , we have to divide $f (x) = 3 x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 3$ by g(x) and get the remainder as shown in the above image.

Hence, $\frac{185}{27}$ should be subtracted from $3 x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 3$ so that the resulting polynomial is exactly divisible by $3 x + 2$ .

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What should be subtracted from 3x4−2x3+3x2−2x+3, so that the resulting polynomial is exactly divisible by (3x+2)?

What should be subtracted from $3 x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 3$ , so that the resulting polynomial is exactly divisible by $(3 x + 2)$ ?