How do find the quotient of #(2x^3 − 3x 2 + x − 6) ÷ (x − 4)#?

How do find the quotient of #(2x^3 − 3x^2 + x − 6) ÷ (x − 4)#?

1 Answer
Aug 11, 2018

Answer:

The quotient polynomial :
#q(x)=2x^2+5x+21 and"the Remainder"=78#

Explanation:

#(2x^3-3x^2+x-6)div(x-4)#

Using synthetic division :

We have , #p(x)=(2x^3-3x^2+x-6) and "divisor : " x=4#

We take ,coefficients of #p(x) to 2,-3,1,-6#

. #4 |# #2color(white)(....)-3color(white)(.......)1color(white)(.......)-6#
#ulcolor(white)(...)|# #ul(0color(white)( .........)8color(white)(.......)20color(white)(.........)84#
#color(white)(....)2color(white)(........)5color(white)(.......)21color(white)(......)color(violet)(ul|78|#
We can see that , quotient polynomial :

#q(x)=2x^2+5x+21 and"the Remainder"=78#

Hence ,

#(2x^3-3x^2+x-6)=(x-4)(2x^2+5x+21 )+(78)#