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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?
• They're all equivalent. For example, finding out when x³-x+1=5 is the same problem as finding out when x³-x-4=0.

We choose 0 to standardize on because if a product of several things is 0, then one of the factors must itself be 0. No other number has this property. This means that factoring the polynomial and finding its solutions are now the same problem.
• Would it be valid to say that instead of the zeroes of the polynomial being the x values that make the polynomial equal to zero, that they could be the x-intercepts that make y = 0 because the polynomial could be written as y = p(x) right?