How do you divide #(v ^ { 2} + v - 39) \div ( v - 6)#?

2 Answers
Narad T.
May 31, 2017

The quotient is #=v+7# and the remainder is #=3#

Explanation:

We perform a long division

#color(white)(aaaa)##v-6##color(white)(aaaa)##|##v^2+v-39##color(white)(aaaa)##|##v+7#

#color(white)(aaaaaaaaaaaaaa)##v^2-6v#

#color(white)(aaaaaaaaaaaaaaa)##0+7v-39#

#color(white)(aaaaaaaaaaaaaaaaa)##+7v-42#

#color(white)(aaaaaaaaaaaaaaaaaaa)##+0+3#

The quotient is #=v+7# and the remainder is #=3#

#(v^2+v-39)/(v-6)=(v+7)+3/(v-6)#

Jim G.
May 31, 2017

#v+7+3/(v-6)#

Explanation:

#"one way is to use the divisor as a factor in the numerator"#

#"consider the numerator"#

#color(red)(v)(v-6)color(magenta)(+6v)+v-39#

#=color(red)(v)(v-6)color(red)(+7)(v-6)color(magenta)(+42)-39#

#=color(red)(v)(v-6)color(red)(+7)(v-6)+3#

#"quotient "=color(red)(v+7)," remander "=3#

#rArr(v^2+v-39)/(v-6)=v+7+3/(v-6)#

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