Remember to write any terms whose coefficient is 0:
color(white)( (x^2+0x-7)/color(black)(x^2+0x-7)) color(white)( (x^4-5x^3+6x^2-10x+15))/( ")" color(white)(")")x^4-5x^3+6x^2-10x+15)x2+0x−7x2+0x−7(x4−5x3+6x2−10x+15)))x4−5x3+6x2−10x+15
Because x^2*x^2 = x^4x2⋅x2=x4, the first term of the quotient is x^2x2:
color(white)( (x^2+0x-7)/color(black)(x^2+0x-7)) (x^2color(white)( 5x^3+6x^2-10x+15))/( ")" color(white)(")")x^4-5x^3+6x^2-10x+15)x2+0x−7x2+0x−7x25x3+6x2−10x+15))x4−5x3+6x2−10x+15
Multiply the first term in the quotient by the divisor and subtract underneath:
color(white)( (x^2+0x-7)/color(black)(x^2+0x-7)) (x^2color(white)( 5x^3+6x^2-10x+15))/( ")" color(white)(")")x^4-5x^3+6x^2-10x+15)x2+0x−7x2+0x−7x25x3+6x2−10x+15))x4−5x3+6x2−10x+15
color(white)(...................)ul(-x^4-0x^3+7x^2)" "darr
color(white)(.........................)-5x^3+13x^2-10x
Because -5x*x^2 =-5x^3. the next term in the quotient is -5x:
color(white)( (x^2+0x-7)/color(black)(x^2+0x-7)) (x^2-5xcolor(white)(6x^2-10x+15))/( ")" color(white)(")")x^4-5x^3+6x^2-10x+15)
color(white)(...................)ul(-x^4-0x^3+7x^2)" "darr
color(white)(.........................)-5x^3+13x^2-10x
Multiply the second term in the quotient by the divisor and subtract underneath:
color(white)( (x^2+0x-7)/color(black)(x^2+0x-7)) (x^2-5xcolor(white)(6x^2-10x+15))/( ")" color(white)(")")x^4-5x^3+6x^2-10x+15)
color(white)(...................)ul(-x^4-0x^3+7x^2)" "darr
color(white)(.........................)-5x^3+13x^2-10x
color(white)(..............................)ul(5x^3+color(white)(.)0x^2-45x)" "darr
color(white)(........................................)13x^2-45x+15
Because 13*x^2 =13x^2. the next term in the quotient is 13:
color(white)( (x^2+0x-7)/color(black)(x^2+0x-7)) (x^2-5x+13color(white)(-10x+15))/( ")" color(white)(")")x^4-5x^3+6x^2-10x+15)
color(white)(...................)ul(-x^4-0x^3+7x^2)" "darr
color(white)(.........................)-5x^3+13x^2-10x
color(white)(..............................)ul(5x^3+color(white)(.)0x^2-45x)" "darr
color(white)(........................................)13x^2-45x+15
Multiply the third term in the quotient by the divisor and subtract underneath:
color(white)( (x^2+0x-7)/color(black)(x^2+0x-7)) (x^2-5x+13color(white)(-10x+15))/( ")" color(white)(")")x^4-5x^3+6x^2-10x+15)
color(white)(...................)ul(-x^4-0x^3+7x^2)" "darr
color(white)(.........................)-5x^3+13x^2-10x
color(white)(..............................)ul(5x^3+color(white)(.)0x^2-35x)" "darr
color(white)(........................................)13x^2-45x+15
color(white)(.....................................)ul(-13x^2color(white)(.)-0x+91)
color(white)(...............................................)-45x+106
The quotient is x^2-5x+13 with a remainder of -45x+10
