Question

Please answer this question.
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Answer 1

       $\underline{\bold{Solution:}}$

       $\text{Let }p(x) = 2x^{3} + x^{2} -ax + 2 \text{, }g(x) = 2x^{3} - 3x^{2} -3x + a\text{ and }f(x) = (x-2)$

       $\text{Let the remainder of }\dfrac{p(x)}{f(x)} \text{ and }\dfrac{g(x)}{f(x)}\text{ be }R_1 \text{ and }R_2 \text{ respectively}$

       $\text{According to the question:}$

       $R_1 = R_2 \text{ ------ (i)}$

       $\text{Refer to the respective attachments for complete steps of long division}$

       $\text{As we can see }R_1 = (22-2a) \text{ and }R_2 = (a-2)$

       $\text{In (i)}$

$\implies 22-2a = a - 2$

       $\text{Transposing terms from R.H.S to L.H.S}$

$\implies 22 - 2a - a + 2 = 0$

       $\text{Simplifying...}$

$\implies 24 - 3a = 0$

       $\text{Transposing } 3a \text{ to R.H.S}$

$\implies 24 = 3a$

       $\text{Transposing } 3 \text{ to L.H.S}$

$\implies \dfrac{24}{3} = a$

       $\text{Simplifying...}$

$\implies \boxed{8 = a}$

Answer 2

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Step-by-step explanation:

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