How do you simplify and divide #(y^3+3y^2-5y-4)/(y+4)#?

2 Answers
Jul 5, 2017

The quotient is #=y^2-y-1#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##-4##color(white)(aaaa)##|##color(white)(aaaa)##1##color(white)(aaaa)##3##color(white)(aaaaa)##-5##color(white)(aaaa)##-4#
#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaa)##-4##color(white)(aaaaaa)##4##color(white)(aaaaaa)##4#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaa)##1##color(white)(aaa)##-1##color(white)(aaaaa)##-1##color(white)(aaaaaa)##color(red)(0)#

The remainder is #0# and the quotient is #=y^2-y-1#

#(y^3+3y^2-5y-4)/(y+4)=y^2-y-1#

Jul 5, 2017

#y^2-y-1#

Explanation:

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

#"consider the numerator"#

#color(red)(y^2)(y+4)color(magenta)(-4y^2)+3y^2-5y-4#

#=color(red)(y^2)(y+4)color(red)(-y)(y+4)color(magenta)(+4y)-5y-4#

#=color(red)(y^2)(y+4)color(red)(-y)(y+4)color(red)(-1)(y+4)color(magenta)(+4)-4#

#=color(red)(y^2)(y+4)color(red)(-y)(y+4)color(red)(-1)(y+4)+0#

#rArr(cancel((y+4))(color(red)(y^2-y-1)))/cancel((y+4))#

#=y^2-y-1larr" quotient"#