Question 254212
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"Linear" means that the largest exponent of x after the right side
is multiplied out and all like terms collected is 1.

"Quadratic" means that the largest exponent of x after the right side
is multiplied out and all like terms collected is 2.

"Cubic" means that the largest exponent of x after the right side
is multiplied out and all like terms collected is 3.

"Quartic" means that the largest exponent of x after the right side
is multiplied out and all like terms collected is 4.

"Quintic" means that the largest exponent of x after the right side
is multiplied out and all like terms collected is 5.

But right now you're only studying the first two, "linear" and "quadratic"

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{{{y=3x-5}}}

That doesn't need to be multiplied out or any terms collected.
And the largest power of x is 1, so it's linear.

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{{{y=(3x-2)(x+6)}}}

That needs to be multiplied out and like terms collected:

{{{y=(3x-2)(x+6)}}}

Use FOIL to multiply it out:

{{{y=3x^2+18x-2x-12}}} 

Collect like terms:

{{{y = 3x^2+16x-12}}}

The largest power of x is 2, so it's quadratic.

[Note: You probably could just have looked at it and seen
that the largest power of x would end up being be 2 if you 
multiplied it out and collected like terms without actually
bothering to to do so.]

Edwin</pre>