Express the series in summation notation. 2 + 4 + 6 + 8 + 10 + 12
2 answers:
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Answer:
see explanation
Step-by-step explanation:
(f + g)(x) = f(x) + g(x), so
f(x) + g(x)
= x² + 5x + 6 + x + 3 ← collect like terms
= x² + 6x + 9
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(f - g)(x) = (f(x) - g(x), so
f(x) - g(x)
= x² + 5x + 6 - (x + 3) ← distribute by - 1
= x² + 5x + 6 - x - 3 ← collect like terms
= x² + 4x + 3
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(f • g)(x)
= f(x) × g(x)
= (x² + 5x + 6)(x + 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x²(x + 3) + 5x(x + 3) + 6(x + 3) ← distribute parenthesis
= x³ + 3x² + 5x² + 15x + 6x + 18 ← collect like terms
= x³ + 8x² + 21x + 18
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( )(x)
=
= ← factor the numerator
= ← cancel common factor (x + 3) on numerator/ denominator
= x + 2