The table below gives the price for different numbers of burgers. Do the numbers in the table represent a proportional relationship?

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  Factor the numerator and the denominator

[ax² + bx + c]

4z² - 16z + 15     Since a > 1, multiply a and c together, then find the factors of (a·c), that adds or subtracts to = b.

(a·c) --> (4 · 15) = 60

Factors of 60:

1 · 60, 2 · 30, 3 · 30, 4 · 15, 5 · 12, 6 · 10  

[The only factor is 6 and 10, (-6) + (-10) = -16] So you substitute -6z - 10z for -16z

4z² - 6z - 10z + 15   Factor out 2z from 4z² - 6z, and factor out -5 from -10z + 15

2z(2z - 3) - 5(2z - 3) Factor out (2z - 3) and your left with:

(2z - 3)(2z - 5)

Do the same for the denominator, and you should get (z - 3)(2z - 5)

Now you have:

  You can cancel out (2z - 5)