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That all depends on the meaning of the context. If you want to determine the values of the polynomial function, then you need to substitute the value for the input variable of the function. Finally, evaluate it. For instance: f(x) = x + 2 If x = 2, then f(2) = 2 + 2 = 4.
Any multiple of X^2+X/2-1/2
Easy. Same thing as the graph of f(x) = x^2 + 1 which have NO intercept.
Yes, 18y3 + 2y2 + 1 is a polynomial; it is a cubic expression. If it were expanded to form an equation, then it would be a cubic equation (or higher), capable of solution.
-2
That all depends on the meaning of the context. If you want to determine the values of the polynomial function, then you need to substitute the value for the input variable of the function. Finally, evaluate it. For instance: f(x) = x + 2 If x = 2, then f(2) = 2 + 2 = 4.
Any multiple of X^2+X/2-1/2
A polynomial of degree 2.
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.
A polynomial function is simply a function that is made of one or more mononomials. For example 4x^2+3x-5 A rational function is when a polynomial function is divided by another polynomial function.
x^2+2x+1
Assuming 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.
It can have 1, 2 or 3 unique roots.
It is x^3 - x^2 - 4x + 4 = 0
A polynomial function of least degree with rational coefficients and a leading coefficient of 1 that has the zeros -7 and -4 can be constructed using the fact that if ( r ) is a zero, then ( (x - r) ) is a factor. Therefore, the polynomial can be expressed as ( f(x) = (x + 7)(x + 4) ). Expanding this, we get ( f(x) = x^2 + 11x + 28 ). Thus, the polynomial function is ( f(x) = x^2 + 11x + 28 ).
To determine the relationship between ( (x - 2) ) and the polynomial ( 2x^3 + x^2 - 3 ), we can perform polynomial division. If ( (x - 2) ) divides the polynomial evenly, then ( (x - 2) ) is a factor of the polynomial. Alternatively, we can evaluate the polynomial at ( x = 2 ); if the result is zero, it confirms that ( (x - 2) ) is a factor. In this case, substituting ( x = 2 ) gives ( 2(2)^3 + (2)^2 - 3 = 16 + 4 - 3 = 17 ), indicating that ( (x - 2) ) is not a factor of the polynomial.
The table shows ordered pairs for a polynomial function, f х f(x) -3 63 --2 8 -1 - 1 0 0 1 -1 2 8 3 63 What is the degree of f?