Answer:
- y = 2x^5 -2x^3 -12x
- degree 5, 3 terms, end behavior: (-∞, -∞), (+∞, +∞)
Step-by-step explanation:
I like to form the product of something like this by multiplying binomial pairs first. The distributive property applies for that (as does FOIL).
... (x^2 -3)(x^2 +2) = x^2·x^2 + x^2·2 + (-3)·x^2 + (-3)·2
... = x^4 -x^2 -6 . . . . . the two x^2 terms combine
Now, it is a simple matter to multiply each term by 2x:
... y = 2x^5 -2x^3 -12x
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The highest-degree term has degree 5. There are 3 terms. (All are odd-degree, so this is an odd function, symmetrical about the origin.)
As with any odd-degree function (with positive leading coefficient) the overall shape has a positive slope (/), tending toward -∞ for large negative values of x, and tending toward +∞ for large positive values of x.
