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What is the definition for the zero of a polynomial function?
The zero of a polynomial in the variable x, is a value of x for which the polynomial is zero. It is a value where the graph of the polynomial intersects the x-axis.
What is a root of a polynomial function?
A value of the variable that makes the polynomial equal to zero (apex)
What is a polynomial that doesn't have any like terms?
zero polynomial which is 0 and only 0 = 0.
If a polynomial is divided by (x-a) and the remainder equals zero then (x-a) is a factor of the polynomial?
false - apex
What is the discriminant of the polynomial below?
That depends on the values of the polynomial but in general:- If the discriminant is greater than zero it has 2 solutions If the discriminant is equal to zero then it has 2 equal solutions If the discriminant is less than zero it has no solutions
Is a polynomial of degree zero is a constant term true or false?
True. A polynomial of degree zero is defined as a polynomial where the highest degree term has a degree of zero. This means that the polynomial is a constant term, as it does not contain any variables raised to a power greater than zero. Therefore, a polynomial of degree zero is indeed a constant term.
Is a polynomial of degree zero a constant term?
Yes.
If you find that a term is missing from a long division polynomial problem you should write that term with a coefficient of?
Zero.
Which mathematical term describes the x-value of a point where the graph of a polynomial crosses the x-axis?
A root or a zero of the polynomial.
What is the definition for the zero of a polynomial function?
The zero of a polynomial in the variable x, is a value of x for which the polynomial is zero. It is a value where the graph of the polynomial intersects the x-axis.
Does a polynomial with a leading term with an even exponent must have at least one real zero?
No.
If you find that a term is missing from a long division polynomial problem how should you write the problem?
zero
Where p is a factor of the leading coefficient of the polynomial and q is a factor of the constant term.?
Anywhere. Provided it is not zero, and number p can be the leading coefficient of a polynomial. And any number q can be the constant term.
What is the leading term in a polynomial?
The leading term in a polynomial is the term with the highest degree, which determines the polynomial's end behavior and its classification (e.g., linear, quadratic, cubic). It is typically expressed in the form ( ax^n ), where ( a ) is a non-zero coefficient and ( n ) is a non-negative integer. The leading term is crucial for understanding the polynomial's growth as the input values become very large or very small.
What is the number which when substituted in a polynomial makes its value zero?
A root.
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.
Why does the constant term of a polynomial written in standard form give you the y intercept of the graph?
In a polynomial written in standard form, the constant term is the value of the polynomial when the input variable (usually (x)) is zero. This means that when you set (x = 0), the polynomial evaluates to the constant term, which corresponds to the point where the graph intersects the y-axis. Therefore, the constant term directly represents the y-intercept of the graph.
