Please help I dont understand how to solve this Given g(x)=3x^2-5x+2 when g(x+2)

Given g(x)=3x^2-5x+2
g(x+2)

answer 3x^2-7x+4

please show work , thank you

g(x) = 3x^2 - 5x + 2

When you are doing g(x), it means for some variable, x, the following equation applies to all variables which are x. So when doing g(3), you replace x with 3 and solve. In this case, we are solving for a variable that consists of a variable and a constant. It's the same procedure though. Substitute x + 2 in all places where an x occurs:

g(x + 2) = 3(x + 2)^2 - 5(x + 2) + 2

Now, expand these by FOIL for the first term, and by distributing for the second:

g(x + 2) = 3(x^2 + 4x + 4) - 5x - 10 + 2

Again, distribute:

g(x + 2) = 3x^2 + 12x + 12 - 5x - 10 + 2

Collect like terms:

g(x + 2) = 3x^2 + (12x - 5x) + (12 - 10 + 2)

When you collect and simplify, you get a final answer:

g(x + 2) = 3x^2 + 7x + 4

g(x)=3x^2-5x+2 when g(x+2)?

g(x)=3(x+2)^2-5(x+2)+2

g(x+2) = 3[x+2]^2-7[x+2]+4
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