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What best describes a root of a polynomial?
A value of the variable when the polynomial has a value of 0. Equivalently, the value of the variable when the graph of the polynomial intersects the variable axis (usually the x-axis).
Why does every polynomial have a real root?
1+x2 is a polynomial and doesn't have a real root.
Is the square root of x a polynomial?
No,
Is it possible to find a polynomial of degree 3 that has -2 as its only real zero?
5
What can the degree of a polynomial tell you about the graph?
The degree is equal to the maximum number of times the graph can cross a horizontal line.
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - a is a factor?
B
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - b is a factor?
a
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - c is a factor?
a
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 best describes a root of a polynomial?
A value of the variable when the polynomial has a value of 0. Equivalently, the value of the variable when the graph of the polynomial intersects the variable axis (usually the x-axis).
What is the number which when substituted in a polynomial makes its value zero?
A root.
How do you graph a polynomial in order to solve for the Zeros?
Either graph the polynomial on graph paper manually or on a graphing calculator. If it is a "y=" polynomial, then the zeroes are the points or point where the polynomial touches the x-axis. If it is an "x=" polynomial, then the zeroes are the points or point where the polynomial touches the y-axis. If it touches neither, then it has no zeroes.
The graph of a polynomial changes direction twice and has only one root What can you say about the polynomial?
It is a polynomial of odd power - probably a cubic. It has only one real root and its other two roots are complex conjugates. It could be a polynomial of order 5, with two points of inflexion, or two pairs of complex conjugate roots. Or of order 7, etc.
What do the zeros of a polynomial function represent on a graph?
The zeros of a polynomial represent the points at which the graph crosses (or touches) the x-axis.
Why does every polynomial have a real root?
1+x2 is a polynomial and doesn't have a real root.
Are a polynomial's factors the values at which the graph of a polynomial meets the x-axis?
false
Are a polynomial's factors the values at which the graph of a polynomial meets the y-axis?
Not quite. The polynomial's linear factors are related - not equal to - the places where the graph meets the x-axis. For example, the polynomial x2 - 5x + 6, in factored form, is (x - 2) (x - 3). In this case, +2 and +3 are "zeroes" of the polynomial, i.e., the graph crosses the x-axis. That is, in an x-y graph, y = 0.
