Find (f + g) (x) and (f g) (x) for f (x) = 6x2 + 5 and g (x) = 7 - 5x.

see explanation

Step-by-step explanation:

(f + g) (x) = f (x) + g (x)

f (x) + g (x)

= 6x² + 5 + 7 - 5x ← collect like terms

= 6x² - 5x + 12

(fg) (x) = f (x) * g (x)

= (6x² + 5) (7 - 5x)

Each term in the second factor is multiplied by each term in the first factor

=6x² (7 - 5x) + 5 (7 - 5x) ← distribute both parenthesis

= 42x² - 30x³ + 35 - 25x

= - 30x³ + 42x² - 25x + 35