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
maganbhai P.
Aug 11, 2018

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)

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