Answer:
The answer is
[tex] {x}^{4} + 4 {x}^{3} - 7 {x}^{2} - 22x + 28[/tex]
[tex](x - 1)(x - 2)(x + 3)(x + 4) + 4[/tex]
[tex](x - 1)(x - 2)[/tex]
[tex]x(x - 2) - 1(x - 2)[/tex]
[tex] {x}^{2} - 2x - 1x + 2[/tex]
[tex] {x}^{2} - 3x + 2[/tex]
[tex](x + 3)(x + 4)[/tex]
[tex]x(x + 4) + 3(x + 4)[/tex]
[tex] {x}^{2} + 4x + 3x + 12[/tex]
[tex] {x}^{2} + 7x + 12[/tex]
Multiplying the both:
[tex]( {x}^{2} - 3x + 2)( {x}^{2} + 7x + 12) + 4[/tex]
[tex] {x}^{2} ( {x}^{2} + 7x + 12) - 3x( {x}^{2} + 7x + 12) + 2( {x}^{2} + 7x + 12) + 4[/tex]
[tex] {x}^{4} + 7 {x}^{3} + 12 {x}^{2} - 3 {x}^{3} - 21 {x}^{2} - 36x + 2 {x}^{2} + 14x + 24 + 4[/tex]
[tex] {x}^{4} + 4 {x}^{3} - 7 {x}^{2} +2x + 28[/tex]
tex] {x}^{4} + 7 {x}^{3} + 12 {x}^{2} - 3 {x}^{3} - 21 {x}^{2} - 36x + 2 {x}^{2} + 14x + 24 + 4[/tex]
tex] {x}^{4} + 7 {x}^{3} + 12 {x}^{2} - 3 {x}^{3} - 21 {x}^{2} - + 2 {x}^{2} + 2x + 28[/tex]
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Answers & Comments
Answer:
The answer is
[tex] {x}^{4} + 4 {x}^{3} - 7 {x}^{2} - 22x + 28[/tex]
Verified answer
☆ANSWER:☆
[tex](x - 1)(x - 2)(x + 3)(x + 4) + 4[/tex]
Splitting the two equations
Equation 1:
[tex](x - 1)(x - 2)[/tex]
[tex]x(x - 2) - 1(x - 2)[/tex]
[tex] {x}^{2} - 2x - 1x + 2[/tex]
[tex] {x}^{2} - 3x + 2[/tex]
Equation 2:
[tex](x + 3)(x + 4)[/tex]
[tex]x(x + 4) + 3(x + 4)[/tex]
[tex] {x}^{2} + 4x + 3x + 12[/tex]
[tex] {x}^{2} + 7x + 12[/tex]
Multiplying the both:
[tex]( {x}^{2} - 3x + 2)( {x}^{2} + 7x + 12) + 4[/tex]
[tex] {x}^{2} ( {x}^{2} + 7x + 12) - 3x( {x}^{2} + 7x + 12) + 2( {x}^{2} + 7x + 12) + 4[/tex]
[tex] {x}^{4} + 7 {x}^{3} + 12 {x}^{2} - 3 {x}^{3} - 21 {x}^{2} - 36x + 2 {x}^{2} + 14x + 24 + 4[/tex]
[tex] {x}^{4} + 4 {x}^{3} - 7 {x}^{2} +2x + 28[/tex]
tex] {x}^{4} + 7 {x}^{3} + 12 {x}^{2} - 3 {x}^{3} - 21 {x}^{2} - 36x + 2 {x}^{2} + 14x + 24 + 4[/tex]
tex] {x}^{4} + 7 {x}^{3} + 12 {x}^{2} - 3 {x}^{3} - 21 {x}^{2} - + 2 {x}^{2} + 2x + 28[/tex]