21.
[tex]a)(x {}^{2} - x)( {x}^{2} - x - 2) + 1 = {x}^{4} - {x}^{3} - 2x {}^{2} - {x}^{3} + {x}^{2} + 2x + 1 = {x}^{4} - 2 {x}^{3} - {x}^{2} + 2x + 1[/tex]
[tex]b)( {x}^{2} + x)( {x}^{2 } + x + 4) + 4 = {x}^{4} + {x}^{3} + 4x {}^{2} + {x}^{3} + {x}^{2} + 4x + 4 = {x}^{4} + {2}^{} x {}^{3} + 5 {x}^{2} + 4x + 4[/tex]
[tex]c)( {x}^{2} + 5x)( {x}^{2} + 5x - 4) + 4 = {x}^{4} + 5 {x}^{3} - 4 {x}^{2} + 5 {x}^{3} + 25 {x}^{2} - 20x + 4 = {x}^{4} + 10 {x}^{3} + 21 {x}^{2} - 20x + 4[/tex]
[tex]d)( {x}^{2} - 7x)( {x}^{2} - 7x - 6) + 9 = {x}^{4} - 7 {x}^{3} - 6 {x}^{2} - 7 {x}^{3} + 49 {x}^{2} + 42x + 9 = {x}^{4} - 14 {x}^{3} + 43 {x}^{2} + 42x + 9[/tex]
