Can anyone help me with any of these and show me how you did them so I can learn, pleasee? Thanks!

Question

Let f(x) = x + 7 and g(x) = x – 2. What is f(x) • g(x)?

x^2 – 5x + 14

x^2 + 5x – 14

x^2 + 5x – 5

x^2 + 9x + 5

What is the quotient: (3x^3 – 16x^2 + 23x – 6) ÷ (3x – 1) ?

x^2 + 5x + 6

x^2 – 5x + 6

–x^2 – 5x – 6

–^x2 + 5x + 6 

Answer 1

Let f(x) = x + 7 and g(x) = x - 2

Then f(x) * g(x) = (x + 7) * (x - 2)

This is in the form (a + b) (c - d) where a = x, b = 7, c = x and d = 2

                           = x*x - x*2 + 7*x - 7*2                     [ Since (a + b) (c - d) = ac - ad + bc - bd ]

                           = x^2 - 2x + 7x - 14                          [ Since a*a = a^2 ]

                           = x^2 + 5x - 14

Therefore the answer is x^2 + 5x - 14

Answer 2

Quotient of (3x^3 - 16x^2 + 23x - 6) / (3x - 1) can be odtained by using synthetic division.

3x - 1 can be written as x - 1/3

             1/3   |    3     -16     23     -6

                     |     0       1      -5      6

                     |________________

                           3    -15    18     |0

=> 3x^2 - 15x + 18                      [ dividing by 3 ]

=> x^2 - 5x +6

Therefore the answer is x^2 - 5x + 6.