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A zero of a polynomial function - or of any function, for that matter - is a value of the independent variable (often called "x") for which the function evaluates to zero. In other words, a solution to the equation P(x) = 0.
For example, if your polynomial is x2 - x, the corresponding equation is x2 - x = 0. Solutions to this equation - and thus, zeros to the polynomial - are x = 0, and x = 1.
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ViviAssuming the polynomial is written in terms of "x": It means, what value must "x" have, for the polynomial to evaluate to zero? For example:
f(x) = x2 - 5x + 6
has zeros for x = 2, and x = 3. That means that if you replace each "x" in the polynomial with 2, for example, the polynomial evaluates to zero.
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A remainder of zero in the process of doing synthetic division tells you that you have found a root of the polynomial function and a factor of the polynomial. A. True?
true
What are the zeros of a polynomial function?
the zeros of a function is/are the values of the variables in the function that makes/make the function zero. for example: In f(x) = x2 -7x + 10, the zeros of the function are 2 and 5 because these will make the function zero.
Why might it be useful to know the linear factors of a polynomial function?
It is useful to know the linear factors of a polynomial because they give you the zeros of the polynomial. If (x-c) is one of the linear factors of a polynomial, then p(c)=0. Here the notation p(x) is used to denoted a polynomial function at p(c) means the value of that function when evaluated at c. Conversely, if d is a zero of the polynomial, then (x-d) is a factor.
Is it possible to add 2 polynomials together and your answer is not a polynomial?
No. Even if the answer is zero, zero is still a polynomial.
What is a zero degree polynomial called?
a polynomial of degree...............is called a cubic polynomial
