Question

Diket polinomial p(x) = (x^ - 2x + 5) (2x^ - x - 3) + mx + n bernilai 4 untuk x = 2 dan bernilai 8 untuk x = 1 . Tentukan nilai :
a. M dan N
b. P(-1)

Answer 1

15 + 2m + n = 4 -->> 2m + n = -11

-8 + m + n = 8 -->> m + n = 16

hasil eliminasi m = -27 dan n = 43

P(-1) = -27.(-1) + 43 = 70

Answer 2

P(x) = (x² -2x+5)(2x² - x - 3) + mx + n
P(2)= 4
(4 -4 +5)(8-2-3) + 2m+n = 4
5(3) + 2m +n = 4
2m + n = -11 .....(pers, 1)

P(1) = 8
(1-2+5)(2-1-3) + m + n = 8
4(-2) +m + n  = 8
m + n = 16 .....(pers. 2)

pers 1 dan pers 2 eliminasi
2m + n =  -11
m + n = 16
kurangkan
m = - 27
n = 16 - m  --> n = 16 +27 = 43
a) m = - 27 dan n = 43

b) P(x) = (x² -2x+5)(2x² -x - 3) - 27x + 43
P(-1) = (1+2+5)(2 +1 - 3) + 27 + 43 
P(-1) = (8)(0) + 27+43
P(-1) = 70