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1. Diketahui f(x) = x³ - 2 ,
maka f(m-3) = (m-3)³ - 2
= m³ - 3(m)²(3) + 3(m)(3)² - 3³ - 2
= m³ - 9m²+ 27m -27 - 2
= m³ - 9m²+ 27m - 29
Jawab
f(m-3) = m³ - 9m²+ 27m - 29
2a. (x+1)(x+3) -2a = x²+ 3x + x + 3 - 2a
= x²+ 4x + (3 - 2a)
= x²+ 4x - (-3 +2a)
= x²+ 4x -1 ( dari diketahui)
Kita dapatkan
-3 + 2a = 1
⇔2a = 1+3
⇔2a = 4
⇔a = 4/2
⇔a = 2
Jawab
Nilai a = 2
2b. (x²+1)(x-5) + 3a = x³ -5x² + x -5 + 3a
= x³ - 5x² + x + 3a - 5
= x³ - 5x² + x + 16( dari diketahui)
maka kita dapatkan
3a - 5 = 16
⇔3a = 16+5
⇔a = 21/3 = 7
Jawab
Nilai a = 7
Catatan:
Jangan lupa hafal rumus-rumus ini:
(A - B)³ = A³ - 3A²B+ 3AB² - B³
dan
(A + B)³ = A³ + 3A²B+ 3AB² + B³
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