How do you divide (x^4-2x^2+10)/(x-1)x4−2x2+10x−1 using long division? What is the quotient and remainder?

1 Answer
maganbhai P.
Aug 13, 2018

Quotient :q(x)=x^3+x^2-x-1Quotient:q(x)=x3+x2−x−1 "and Remainder " :r(x)=9and Remainder :r(x)=9

Explanation:

Here ,

Dividend :color(blue)(x^4+0x^3-2x^2+0x+10 and:x4+0x3−2x2+0x+10and divisor : color(red)(x-1):x−1

So ,
color(white)(..............................)ul(x^3+x^2-x-1color(white)(.........))larrquotient
color(white)(..................)(x-1) | x^4+0x^3-2x^2+0x+10

color(white)(......)color(violet)((x-1)*x^3tocolor(white)(......)ul(x^4-x^3)color(white)(.......)lArr"subtract"
color(white)(........................................0)x^3-2x^2

color(white)(..........)color(violet)((x-1)*x^2tocolor(white)(.......)ul(x^3-x^2)color(white)(.......)lArr"subtract"
color(white)(...............................................)-x^2+0x

color(white)(.......................)color(violet)((x-1)(-x))color(white)(......)ul(-x^2+x)color(white)(.......)lArr"subtract"
color(white)(.......................................................)-x+10

color(white)(.................color(violet)((x-1)(-1))...................)ul(-x+1)color(white)(...)lArr"subtract"

color(white)(...................................................................)9larr"Remainder"

Hence ,

(color(blue)(x^4+0x^3-2x^2+0x+10))=(x-1)(x^3+x^2-x-1)+9

Quotient :q(x)=x^3+x^2-x-1 "and Remainder " :r(x)=9

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