Materi suku banyak kelas 11 sma

f(x) = h(x).b(x) + s(x)
f(x) = persamaan
h(x) = hasil
b(x) = pembagi
s(x) = sisa

[tex]f(x) = 3 {x}^{3} + 8 {x}^{2} - x - 9 \\b(x) = {x}^{2} + 2x - 3 \\ b(x) = (x + 3)(x - 1) \\ b(x) \: nya \: difaktorkan[/tex]
[tex]f(x) = h(x).b(x) + s(x) \\ 3 {x}^{3} + 8 {x}^{2} - x - 9 = h(x).( x + 3)( x - 1) + (ax + b)\\ \\ x = - 3 \\3( { - 3}^{3} ) + 8( { - 3}^{2} ) + 3 - 9 = 0 - 3a + b \\ - 81 + 72 + 3 - 9 = - 3a + b \\ -15 = - 3a + b \\ \\ x = 1 \\ 3( {1}^{3} ) + 8( {1}^{2} ) - 1 - 9 = a + b \\ 3 + 8 - 1 - 9 = a + b \\ 1 = a + b[/tex]

eliminasi
[tex] - 15 = - 3a + b \\ 1 \: \: \: \: \: = a + b \\ - - - - - - - - \: \: - (dikurangin) \\ - 16 = - 4a \\ a = \frac{ - 16}{ - 4} = 4 \\ \\ a + b = 1 \\ 4 + b = 1 \\ b = 1 - 4 = - 3[/tex]
[tex]s(x) = ax + b \\ = 4x - 3( \times - 1) = - 4x + 3[/tex]
jawabannya C
maap kalo salah
semoga membantu