Diketahui suku banyak p(x) = (x² − 2x + 5)(2x² − x − 3) + mx + n bernilai 4 untuk x = 2 dan bernilai 8 untuk x = 1. Tentukan nilai: a. m dan n b. p(−1)

Suku Banyak

p(x)= (x² -2x+5)(2x²-x-3) +mx + n
p(2) = 5 --> (4-4+5)(8-2-3) +m(2) +n =5
5(3) + 2m + n = 5 --> 15 + 2m + n = 5
2m + n = -10 ..(1)

p(1)= 8 --> (1-2+5)(2-1-3) + m(1) + n = 8
4(-2) + m + n = 8
m + n = 16.....(2)
.
2m + n = -10
m + n = 16
kurangkan
m = - 26

m+n = 16
n = 16  - m = 16 - (-26) = 42

m = -26 dan n  = 42

b.
p(x) = (x² - 2x +5)(2x²-x-3) - 26 x + 42
p(-1) = (1 +2+5)(2+1 -3) + 26 + 42
p(-1) = 8(0) + 68
p(-1) = 68
...