If x+1 is a factor of 2x^{3}+ax^{2}+2bx+1,the | vedclass

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(D) Given that $(x+1)$ is a factor of $f(x) = 2x^{3} + ax^{2} + 2bx + 1$,by the Factor Theorem,$f(-1) = 0$.Substituting $x = -1$ into the polynomial:$

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$5, 2$

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(D) Given that $(x+1)$ is a factor of $f(x) = 2x^{3} + ax^{2} + 2bx + 1$,by the Factor Theorem,$f(-1) = 0$.Substituting $x = -1$ into the polynomial:$2(-1)^{3} + a(-1)^{2} + 2b(-1) + 1 = 0$$-2 + a - 2b + 1 = 0$$a - 2b = 1$ ... $(i)$We are also given the equation $2a - 3b = 4$ ... $(ii)$.From equation $(i)$,we have $a = 2b + 1$.Substituting this into equation $(ii)$:$2(2b + 1) - 3b = 4$$4b + 2 - 3b = 4$$b + 2 = 4$$b = 2$Now,substitute $b = 2$ into $a = 2b + 1$:$a = 2(2) + 1 = 5$.Thus,the values are $a = 5$ and $b = 2$.

If $x+1$ is a factor of $2x^{3}+ax^{2}+2bx+1$,then find the values of $a$ and $b$ given that $2a-3b=4$.

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