Question

what is the remainder when
$2 {x}^{3} - 3 {x}^{2} + 3x \div 2x + 1$

Answer 1

Heya !!!


P(X) = 2X³ - 3X² + 3X




G(X) = 2X +1




On dividing P(X) by G(X) we get,




2X +1 ) 2X³ -3X² + 3X ( X² - 2X

----------2X³ + X²

*******_-___-______

*******0*****-4X² + 3X

----------------4X² -2X

*********__+____+_____

***************0****5X




Hence,


Remainder = 5X And Quotient = X² -2X.




HOPE IT WILL HELP YOU...... :-)

Answer 2

$let \: he \: polynomial \: be \: p(x) = 2 {x}^{3} - 3 {x}^{2} + 3x. \\ the \: zero \: is \: = 2x + 1 = 0 = > x = \frac{ - 1}{2} \\ by \: putting \: the \: value \: of \: p( \frac{ - 1}{2} ) \\ = 2 ( { \frac{ - 1}{2} )}^{3} - 3 {( \frac{ - 1}{2} )}^{2} + 3( \frac{ - 1}{2} )\\ = 2 \times \frac{ - 1}{8} - 3 \times \frac{ 1}{4} + \frac{3}{2} \\ = \frac{ - 1}{4} - \frac{3}{4} + \frac{3}{2} \\ = \frac{ - 1 - 3 + 6}{4} = \frac{3}{4} is \: the \: remainder$
hope it's helpful.... sorry for any mistake. .....thanks.,