If the quotient of two polynomials is #4x^2-x-7+(11x+15)/(x^2+x+2)#, what are the two polynomials?

1 Answer
Apr 2, 2017

Answer:

#(4x^4 +3x^3+0x^2+2x+1) -: (x^2+x+2)#

Explanation:

Given:#" "4x^2-x-7+(11x+15)/(x^2+x+2)#

The #11x+15# is the remainder so the denominator must be the divisor. Thus we need to build each term by using #x^2+x+2#

Note that I use a place holder. For example: #0x^4#

color(white)(.)

#4x^2(x^2+x+2) -> 4x^4+4x^3+8x^2#
#-x(x^2+x+2)->0x^4-color(white)(4)x^3-color(white)(8)x^2-2x#
#-7(x^2+x+2)->0x^4+0x^3-7x^2-7x-14#
#"The remainder"->ul(color(white)(.)0x^4+0x^3+0x^2+11x+15) larr" Add" #
#" "4x^4 +3x^3+0x^2+2x+1#