Answer:
y = 17(2)^x
Step-by-step explanation:
If the graph of y = ab^x goes through (0, 17), then
17 = ab*0, or a = 17
Then the function is y = ab^x with a = 17, or
y = 17*b^x and we must find b.
If the graph of y = 17*b^x also goes through (6, 1088), then the following must be true: 1088 = 17*b^6
which reduces to 64 = b^6
Taking the sixth root of both sides, we get 64^(1/6) = b, and so b = 2
Then the desired exponential function is
y = 17(2)^x
We need to find two numbers that multiply to 24 (last coefficient) and add to 10 (middle coefficient). Through trial and error, the two values are 6 and 4
6 + 4 = 10
6*4 = 24
So we can break up the 10ab into 6ab+4ab and then use factor by grouping
a^2 + 10ab + 24b^2
a^2 + 6ab + 4ab + 24b^2
(a^2+6ab) + (4ab+24b^2)
a(a+6b) + 4b(a+6b)
(a+4b)(a+6b)
Therefore, the original expression factors completely to (a+4b)(a+6b)
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