Bank Soal Matematika SMA Teorima Sisa dan Teorema Faktor

Soal

Pilgan

Pembahasan

Penjabaran dari $\frac{x ^{5} + 1 0 2 4}{x + 4}$ adalah ....

A

$x^{4} - 4 x^{3} + 16 x^{2} - 64 x + 256$

B

$x^{4} + 4 x^{3} + 16 x^{2} + 64 x + 256$

C

$- x^{4} + 4 x^{3} - 16 x^{2} + 64 x - 256$

D

$- x^{4} - 4 x^{3} - 16 x^{2} - 64 x - 256$

E

$x^{4} - 4 x^{3} + 16 x^{2} - 64 x - 256$

Pembahasan:

Gunakan aturan pembagian istimewa $\frac{a^{2n+1}+b^{2n+1}}{a+b}=a^{2n}b^0-\ a^{2n-1}b^1+a^{2n-2}b^2-a^{2n-3}b^3+a^0b^{2n}$ , dimana $a=x\ ,\ b=4\ \text{dan}\ n=2$

$\Leftrightarrow\frac{a^{2n+1}+b^{2n+1}}{a+b}=a^{2n}b^0-\ a^{2n-1}b^1+a^{2n-2}b^2-a^{2n-3}b^3+a^0b^{2n}$

$\Leftrightarrow\frac{x^5+1024}{x+4}=x^{2\left(2\right)}4^0-\ x^{2\left(2\right)-1}4^1+x^{2\left(2\right)-2}4^2-x^{2\left(2\right)-3}4^3+x^04^{2\left(2\right)}$