Question

Please help ASAP!!!!!!

Answer 1

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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($\frac{f}{g}$ )(x)

= $\frac{f(x)}{g(x)}$

= $\frac{x^2+5x+6}{x+3}$ ← factor the numerator

= $\frac{(x+2)(x+3)}{x+3}$ ← cancel common factor (x + 3) on numerator/ denominator

= x + 2