Question

5. If the polynomial p(x) = x³- x²+ 3x + k is divided by (x - 1), the remainder obtainedis 3, then the value of k is​

Answer 1

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow p(x)=x^3-x^2+3x+k$

$\sf\dashrightarrow g(x)=x-1$

$\sf\implies x-1=0$

$\sf\implies x=1$

$\sf\dashrightarrow remainder\:obtained\:when\:p(x)\: get's\:divided\:by\:g(x)\:is\:3$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow THE\:VALUE\:OF\:K$

$\large\underline\bold{SOLUTION,}$

$\sf\therefore x^3-x^2+3x+k=3\:----[AS\:GIVEN\:]$

$\sf\implies (1)^3-(1)^2+3(1)+k=3$

$\sf\implies 1-1+3+k=3$

$\sf\implies \cancel{ 1} \: \cancel{-1}+3+k=3$

$\sf\implies 3+k=3$

$\sf\implies k=3-3$

$\sf\implies k=0$

$\large{\boxed{\bf{\star\:\: k=0 \:\: \star }}}$

$\large\underline\bold{\therefore \: THE\:VALUE\:OF\:'K'\:IS\:0}$

____________________

Answer 2

$\large\underline{\underline{\bold{\pink{\mathfrak{AnSwEr}}}}}$

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow p(x)=x^3-x^2+3x+k$

$\sf\dashrightarrow g(x)=x-1$

$\sf\implies x-1=0$

$\sf\implies x=1$

$\sf\dashrightarrow remainder\:obtained\:when\:p(x)\: get's\:divided\:by\:g(x)\:is\:3$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow THE\:VALUE\:OF\:K$

$\large\underline\bold{SOLUTION,}$

$\sf\therefore x^3-x^2+3x+k=3\:----[AS\:GIVEN\:]$

$\sf\implies (1)^3-(1)^2+3(1)+k=3$

$\sf\implies 1-1+3+k=3$

$\sf\implies \cancel{ 1} \: \cancel{-1}+3+k=3$

$\sf\implies 3+k=3$

$\sf\implies k=3-3$

$\sf\implies k=0$

$\large{\boxed{\bf{\star\:\: k=0 \:\: \star }}}$

$\large\underline\bold{\therefore \: THE\:VALUE\:OF\:'K'\:IS\:0}$