How do you simplify and divide #(y^3+3y^2-5y-4)/(y+4)#?
2 Answers
The quotient is
Explanation:
Let's perform the synthetic division
The remainder is
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"#