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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([tex]\frac{f}{g}[/tex] )(x)
= [tex]\frac{f(x)}{g(x)}[/tex]
= [tex]\frac{x^2+5x+6}{x+3}[/tex] ← factor the numerator
= [tex]\frac{(x+2)(x+3)}{x+3}[/tex] ← cancel common factor (x + 3) on numerator/ denominator
= x + 2
