x^2+2x=3
x^4+7x^3+8x^2-13x+15
=x^2(x^2+2x)+5x^3+8x^2-13x+15
=3x^2+8x^2-13x+15+5x^3
=5x(x^2+2x)+x^2-13x+15
=15x+x^2-13x+15
=x^2+2x+15
=18
x^2+2x=3
x^4+7x^3+8x^2-13x+15
=x^2(x^2+2x)+5x^3+8x^2-13x+15
=3x^2+8x^2-13x+15+5x^3
=5x(x^2+2x)+x^2-13x+15
=15x+x^2-13x+15
=x^2+2x+15
=18