Question

Diketahui suku banyak p(x) = 4x³ - 2x² + x - 4 dan q(x) = x pangkat 4 - 3x² - 5x + 2.
a.tentukan r(x) = 2p(x) + q(x) !
b.tentukan nilai p(-1), q(-1), dan r(-1) !
c. apakah 2p(-1) + q(-1) = r(-1) ?

Answer 1

P(x) = 4x^3 - 2x^2 + x  - 4
q(x) = x^4 - 3x^2 - 5x + 2
a) r(x) = 2p(x) + q(x)
= 2(4x^3 - 2x^2 + x - 4) + x^4 - 3x^2 - 5x + 2
= x^4 + 8x^3 - 7x^2 - 3x - 6
b) nilai :
p(-1) = 4(-1)^3 - 2(-1)^2 + (-1) - 4 = -4 - 2 - 1 - 4 = -11
q(-1) = (-1)^4 - 3(-1)^2 - 5(-1) + 2 = 1 - 3 + 5 + 2 = 5
r(-1) = (-1)^4 + 8(-1)^3 - 7(-1)^2 - 3(-1) - 6 = 1 - 8 - 7  + 3 - 6 = -17
c) 2p(-1) + q(-1) = r(-1)
2(-11) + 5 = -17
-22 + 5 = - 17
-17 = - 17
(BENAR)

 

Answer 2

A) r(x) = 2p(x) + q(x)
= 2(4x³ - 2x² + x - 4) + (x⁴ - 3x² - 5x + 2)
= 8x³ - 4x² + 2x - 8 + x⁴ - 3x² - 5x + 2
= x⁴ + 8x³ - 7x² - 3x - 6

b) p(-1) = 4(-1)³ - 2(-1)² + 1 - 4
= - 4 - 2 + 1 - 4
= -9
q(-1) = (-1)⁴ - 3(-1)² - 5(-1) + 2
= 1 - 3 + 5 + 2
= 5
r(-1) = (-1)⁴ + 8(-1)³ - 7(-1)² - 3(-1) - 6
= 1 - 8 - 7 + 3 - 6
= -17

c) 2p(-1) + q(-1) = r(-1)
2(-9) + 5 = -17
- 13 ≠ -17 (Pernyataan salah)