Question

find the remainder when 3 x cube minus 4 x square + 7 x minus 5 is divided by X + 3
​

Answer 1

${ \boxed{ \mathbf{g(x) = x - 3}}} \\ { \boxed{ \mathbf{p(x) = {3x}^{3} - {4x}^{2} + 7x - 5}}}$

Here,

${ \mathtt{g(x) = > x - 3 = 0 }} \\ { \mathtt{ \: \: \: \: \: \: \: \: \: = > \: \: \: \: \: \: \: \: x = 3 }}$

Now,

${ \mathtt{p(3) = 3{(3)}^{3} - 4 {(3)}^{2} + 7(3) - 5 }} \\ { \mathtt{ \: \: \: \: \: \: \: \: \: = (3 \times 27) - (4 \times 9) + 21 - 5 }} \\ { \mathtt{ \: \: \: \: \: \: \: \: \: =81 - 36 + 21 - 5}} \\ { \mathtt{ \: \: \: \: \: \: \: \: \: =102 - 41 = { \red{61}}}}$

Hence,

${ \boxed{ \huge{ \text{We found that}}}} \\{ \boxed{ \huge{ \text{the required}}}} \\{ \boxed { \huge{ \text{remainder is 61.}}}}$