NOMOR 1.
[tex]a. \: (f + g)(x) = f(x) + g(x)[/tex]
[tex](f + g)(x) = ({x}^{3} - {2x}^{2} + 3x + 1) + ({2x}^{3} - x + 3)[/tex]
[tex](f + g)(x) = {x}^{3} - {2x}^{2} + 3x + 1 + {2x}^{3} - x + 3[/tex]
[tex](f + g)(x) = {x}^{3} + {2x}^{3} - {2x}^{2} + 3x - x + 1 + 3[/tex]
[tex](f + g)(x) = {3x}^{3} - {2x}^{2} + 2x + 4[/tex]
[tex]b. \: (f - g)(x) = f(x) - g(x)[/tex]
[tex](f - g)(x) = ({x}^{3} - {2x}^{2} + 3x + 1) - ({2x}^{3} - x + 3)[/tex]
[tex](f - g)(x) = {x}^{3} - {2x}^{2} + 3x + 1 - {2x}^{3} + x - 3[/tex]
[tex](f - g)(x) = {x}^{3} - {2x}^{3} - {2x}^{2} + 3x + x + 1 - 3[/tex]
[tex](f - g)(x) = { -x}^{3} - {2x}^{2} + 4x - 2[/tex]
[tex](f - g)(x) = - ({x}^{3} + {2x}^{2} - 4x + 2)[/tex]
NOMOR 2.
[tex](f \times g)(x) = f(x).g(x)[/tex]
[tex](f \times g)(x) = ({2x}^{2} - 3x + 1)(x + 3)[/tex]
[tex](f \times g)(x) = ({2x}^{2})(x + 3) + ( - 3x)(x + 3) + (1)(x + 3)[/tex]
[tex](f \times g)(x) = {2x}^{3} + {6x}^{2} - {3x}^{2} - 9x + x + 3[/tex]
[tex](f \times g)(x) = {2x}^{3} + {3x}^{2} - 8x + 3[/tex]
NOMOR 3.
[tex]a. \: p(x) = {x}^{3} - {2x}^{2} + 1[/tex]
[tex]p(2) = {(2)}^{3} - {2 \times (2)}^{2} + 1[/tex]
[tex]p(2) = 8 - 2 \times 4 + 1[/tex]
[tex]p(2) = 8 - 8 + 1[/tex]
[tex]p(2) = 0 + 1[/tex]
[tex]p(2) = 1[/tex]
[tex]b. \: p(x) = {x}^{3} - {2x}^{2} + 1[/tex]
[tex]p( - 3) = {( - 3)}^{3} - {2 \times ( - 3)}^{2} + 1[/tex]
[tex]p( - 3) = ( - 27) - 2 \times 9 + 1[/tex]
[tex]p( - 3) = ( - 27) - 18 + 1[/tex]
[tex]p( - 3) = ( - 45) + 1[/tex]
[tex]p( - 3) = ( - 44)[/tex]
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