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Sketch the graph of a polynomial:
Solution:
Consider the given equation above
Did you notice that the given equation has a common factor which is x⁵? Let's factor the above equation as follows
and then it is factorable by the difference of two squares as follows
If we set y = 0, then the x-intercepts of the given equation are 0, -3, and 3.
If we set x = 0, then the y-intercept of the given equation is
Since we now the x-intercept, then we can sketch the location or direction of a curve as follows
If x < -3, then y = (-)³(-)(-) = (-)
If -3 < x < 0, then y = (-)³(+)(-) = (+)
If 0 < x < 3, then y = (+)³(+)(-) = (-)
If x > 3, then y = (+)³(+)(+) = (+)
Here's the graph of a polynomial:
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| Photo by Math Principles in Everyday Life |