Question

Find the reaminder when y3-y2-2y+5 is divided by y-4​

Answer 1

AnswEr:-

❀ Your Answer Is 45.

ExplanaTion:-

Given polynomial:-

$\\ \tt\longrightarrow {y}^{3} - {y}^{2} - 2y + 5.$

And we have to divide it by x-4.

To Find:-

• The Remainder.

So Now,

• Here we can find out Remainder by two methods:-

1) Long Division Method.

2) Remainder Theorem.

By Long Division Method:-

$\boxed{\begin{array}\quad\begin{tabular}{m{3.5em}cccc}&& y^2& + 3y&+10\\\cline{3-6}\multicolumn{2}{l}{y - 4\big)}& y^3& - y^2& - 2y & + 5\\&& - y^3& - 4y^2&&\\&&(-)& (+) &&\\ \cline{3-6}&&& 3y^2& - 2y& + 5\\&&&3y^2& - 12y &\\ &&& (-) &(+)&\\ \cline{4-6}&&&& 10y& + 5\\&&&&10y& - 40\\ &&&&(-)& (+)\\ \cline{4 - 6}&&&&&45 = remainder. \\\cline{4 - 6} \\\end{tabular}\end{array}}$

Therefore the Remainder is 45.

By Remainder Theorem:-

By Remainder Theorem we get,

$\\ \tt\mapsto y - 4 = 0. \\ \\ \tt\mapsto y = 4.$

By putting the value of y in the polynomial we get:-

$\\ \tt\mapsto {y}^{3} - {y}^{2} - 2y + 5. \\ \\ \tt = (4) {}^{3} - {(4)}^{2} - 2(4) + 5. \\ \\ \tt = 64 - 16 - 8 + 5. \\ \\ \tt = 64 - 24 + 5. \\ \\ \tt = 40 + 5. \\ \\ \tt = 45 = \rm remainder.$

Therefore the Remainder is 45.

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \blue{Question:-}}}}}}$

Find the reminder when y³-y²-2y+5 is divided by y-4 ..

_______________

${ \huge{ \bold{ \underline{ \underline{ \pink{Answer:-}}}}}}$

★ Refer to Attachment ★

✒Verification : -

$\dashrightarrow\sf{y-4}$

$\dashrightarrow\sf{y=4}$

✒Substituting Values : -

$\dashrightarrow\sf{{(4)}^{3}-{(4)}^{2}-2(4)+5}$

$\dashrightarrow\sf{64-16-8+5}$

$\dashrightarrow\sf{64-24+5}$

$\leadsto\sf{{ \large{ \boxed{ \bold{ \bold{ \red{45}}}}}}}$

➴ HENCE VERIFIED ➴