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# Zeros of polynomials: plotting zeros

When we are given a polynomial in factored form, we can quickly find the polynomial's zeros. Then, we can represent them as the x-intercepts of the polynomial's graph.

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• I'm from Russia and berly know English so if you can help me understand the first part.....Thanks... If you can translate it to English that would be great.. I use google translate.
• So basically every polynomial function has "zeros" and these are also called x-intercepts. Zeros are when a polynomial function "intersects" or touches the x-axis. When a polynomial is in factored form, like the question in the video, it is very easy to find the zeros. If you think about it, an x-intercept is when a function intersects the x-axis, and for this to be true, the y-value of that coordinate must be equal to zero. So to solve we can use this property -
If (A)(B)(C) = 0
Then either A, B or C must be = 0
So in the case of 2x(2x+3)(x-2), we just set "A" "B" and "C" as equal to zero, when -
A = 2x = 0
B = 2x+3 = 0
C = x-2 = 0
Now we just solve for x to get our zeros!
We are now left with
x = 0
x = -3/2
x = 2
I hope this helped, If this confused you more or if something seems unclear, please let me know, I'm happy to help!
• why do we need to equal the polynomial to 0 always? why cant it be some other number?
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