By the Remainder Theorem,find the remainder w | vedclass

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(A) According to the Remainder Theorem,if a polynomial $p(x)$ is divided by $g(x) = ax + b$,the remainder is $p(-b/a)$.Set $g(x) = 0$ to find the valu

Vedclass · Accepted Answer

$\frac{-136}{27}$

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(A) According to the Remainder Theorem,if a polynomial $p(x)$ is divided by $g(x) = ax + b$,the remainder is $p(-b/a)$.Set $g(x) = 0$ to find the value of $x$:$1 - \frac{3}{2}x = 0$$\frac{3}{2}x = 1$$x = \frac{2}{3}$Now,substitute $x = \frac{2}{3}$ into $p(x)$:$p\left(\frac{2}{3}\right) = \left(\frac{2}{3}\right)^{3} - 6\left(\frac{2}{3}\right)^{2} + 2\left(\frac{2}{3}\right) - 4$$p\left(\frac{2}{3}\right) = \frac{8}{27} - 6\left(\frac{4}{9}\right) + \frac{4}{3} - 4$$p\left(\frac{2}{3}\right) = \frac{8}{27} - \frac{24}{9} + \frac{4}{3} - 4$To add these,find the common denominator,which is $27$:$p\left(\frac{2}{3}\right) = \frac{8}{27} - \frac{72}{27} + \frac{36}{27} - \frac{108}{27}$$p\left(\frac{2}{3}\right) = \frac{8 - 72 + 36 - 108}{27}$$p\left(\frac{2}{3}\right) = \frac{-136}{27}$

By the Remainder Theorem,find the remainder when $p(x)$ is divided by $g(x)$,where $p(x) = x^{3} - 6x^{2} + 2x - 4$ and $g(x) = 1 - \frac{3}{2}x$.

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