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Formation of Algebraic Expressions

Find the poly...

Question

Find the polynomial which will be obtained by subtracting the quotient from remainder, when $(7 + 15 x - 13 x^{2} + 5 x^{3})$ is divided by $(4 - 3 x + x^{2})$ .

4 x + 3

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- 4 x - 3

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Both (A) and (B)

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None of these

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Solution

The correct option is B $- 4 x - 3$
Let's use long division to divide $7 + 15 x - 13 x^{2} + 5 x^{3}$ by $4 - 3 x + x^{2}$
We get quotient $(Q) = 5 x + 2$ and remainder $(R) = x - 1$
Then, the subtracting quotient from remainder is $Q - R$ or $R - Q$
i.e. $x - 1 - 5 x - 2 = - 4 x - 3$
Hence, B is correct.

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5

If the polynomials $a x^{3} + 4 x^{2} + 3 x - 4$ and $x^{3} - 4 x + a$ leave the same remainder when divided by $x - 3$ , find the value of a ?

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