Question

Please help ASAP!!!!!!

Answer 1

see explanation

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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(
`(f)/(g)` )(x)

=
`(f(x))/(g(x))`

=
`(x^2+5x+6)/(x+3)` ← factor the numerator

=
`((x+2)(x+3))/(x+3)` ← cancel common factor (x + 3) on numerator/ denominator

= x + 2