koefisien X² pada polinomial (x - 1)² (x+2) (x + 1)

Materi : Polinomial
Kelas : X

(x-1)² (x+2) (x+1)
= (x-1)(x-1) (x+2)(x+1)
= (x²-2x+1)(x²+3x+2)
= x⁴+3x³+2x²-2x³-6x²-4x+x²+3x+2
= x⁴ + 3x³ - 2x³ + 2x² - 6x² + x² - 4x + 3x + 2
= x⁴ + x³ - 3x² - x + 2

Ehingga dengan mudah didapat koefisien x² adalah - 3

Semoga Membantu..

[tex] {(x - 1)}^{2} (x + 2)(x + 1) = ... \\ = ( {x}^{2} - 2x + 1)( {x}^{2} + x + 2x + 2) \\ = ( {x}^{2} - 2x + 1)( {x}^{2} + 3x + 2) \\ = {x}^{2} ( {x}^{2} + 3x + 2) \\ - 2x( {x}^{2} + 3x + 2) \\ + 1( {x}^{2} + 3x + 2) \\ \\ = {x}^{4} + {3x}^{3} + 2 {x}^{2} \\ - {2x}^{3} - 6 {x}^{2} - 4x \\ + {x}^{2} + 3x + 2 \\ \\ = {x}^{4} + {x}^{3} - 3 {x}^{2} - x + 2 \\ \\ koefisien \: \\ {x}^{4} = 1 \\ {x}^{3} = 1 \\ {x}^{2} = - 3 \\ x = - 1 \\ konstanta = 2[/tex]
Jadi, koefisien x² = -3