Question

please help me please yaar please ​

Answer 1

$\huge \fbox \purple{Answer (i)}$

$\textbf{Given:-} \: (x + 1)\text{ \: is \: a \: factor \: of} \: {2x}^{3} - 3 {x}^{2} - 8x - 3$

$\fbox{Solve:}$

$\text{if \: } x + 1 \: \text{is \: factor \: of \: \: } {2x}^{3} - 3 {x}^{2} - 8x - 3$

$\textbf{Then Putting on}$

$⇒x + 1 = 0$

$⇒x = - 1⇒f( - 1) = 0$

$⇒f( - 1) = 2( - 1 {)}^{3} - 3( - 1 {)}^{2} - 8( - 1) - 3$

$⇒ - 2 - 3 + 8 - 3$

$⇒f( - 1) = 0$

$\textbf{Hence} \: (x + 1) \: \text{is \: a \: factor \: of \: } {2x}^{3} - 3 {x}^{2} - 8x - 3$

$\huge \fbox \blue{Answer (ii)}$

$\textbf{Given:-} (2x + 3) \: \text{is \: a \: factor \: of \: } {4x}^{3} + {20x}^{2} + 33x + 18$

$\fbox{Solve:}$

$\text{if} \: (2x + 3) \: \text{is \: a \: factor \: of \: } {4x}^{3} + {20x}^{2} + 3x + 18$

$\textbf{Then Putting on}$

$⇒2x + 3 = 0$

$⇒x = \frac{ - 3}{2} ⇒f \left( \frac{ - 3}{2} \right) \] = 0$

$⇒f \left( \frac{ - 3}{2} \right) \] = 4 {\left( \frac{ - 3}{2} \right) \] }^{3} + 20 {\left( \frac{ - 3}{2} \right) \] }^{2} + 33\left( \frac{ - 3}{2} \right) \] + 18$

$⇒85 + 45 - 49.5 + 18$

$= f\left( \frac{ - 3}{2} \right) \] = 0$

$\\ \\ \\ \\ \sf \colorbox{lightgreen} {\red★ANSWER ᵇʸɴᴀᴡᴀʙﷻ}$