Matematika f(x)=4x²-3x⁴+2x-6 g(x)=2x³+5x⁴-2x²+1 h(x)=3x²+5x tentukan: f(x)+g(x) f(x)-g(x) f(x)×h(x)​

electabernhardulv – March 05, 2023

f(x)=4x²-3x⁴+2x-6

g(x)=2x³+5x⁴-2x²+1

h(x)=3x²+5x

tentukan:

f(x)+g(x)

f(x)-g(x)

f(x)×h(x)​

Jawab:

a.  [tex]2x^{4} + 2x^{3} +2x^{2} +2x - 5[/tex]

b.  [tex]-8x^{4}-2x^{3} + 6x^{2} +2x -7[/tex]

c. [tex]-9x^{6} -15x^{5} 12x^{4} +26x^{3} +4x^{2} -30x[/tex]

Penjelasan dengan langkah-langkah:

f(x) + g(x) = ([tex]4x^{2} -3x^{4} +2x -6[/tex] )+ ([tex]2x^{3} + 5x^{4} - 2x^{2} +1[/tex] )= [tex]2x^{4} + 2x^{3} +2x^{2} +2x - 5[/tex]

f(x)-g(x) =  ([tex]4x^{2} -3x^{4} +2x -6[/tex]) - ( [tex]2x^{3} + 5x^{4} - 2x^{2} +1[/tex] )=  [tex]4x^{2} -3x^{4} +2x-6 -2x^{3} -5x^{4} + 2x^{2} - 1[/tex] = [tex]-8x^{4}-2x^{3} + 6x^{2} +2x -7[/tex]

f(x)×h(x)​ = (4x²-3x⁴+2x-6) * (3x²+5x) = [tex]12x^{4} +20x^{3} -9x^{6} -15x^{5} +6x^{3} +10x^{2} -6x^{2} -30x[/tex]

= [tex]-9x^{6} -15x^{5} 12x^{4} +26x^{3} +4x^{2} -30x[/tex]

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