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How do you write a polynomial function with rational coefficients in standard form with given zeros of -1 -1 1?
The polynomial is (x + 1)*(x + 1)*(x - 1) = x3 + x2 - x - 1
What is a zero of polynomial function?
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.
Which is a third degree polynomial with -1 and 1 as its only zeros?
You need to multiply three terms, one for each zero. To have only two zeros, the polynomial would need to have a "double zero" (or more generally, a "multiple zero), that is, a repeated factor. In this case, the zeros can be one of the following: -1, -1, 1, with the corresponding factors: (x+1)(x+1)(x-1) or: -1, 1, 1, with the corresponding factors: (x+1)(x-1)(x-1) If you like, you can multiply these factors out to get the polynomial in standard form.
What is the difference between the polynomial and multinomial?
A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication operations. It typically has one or more terms, each of which can have a different degree. A multinomial, on the other hand, is a specific type of polynomial that has more than one term with multiple variables raised to different powers. In essence, all multinomials are polynomials, but not all polynomials are multinomials.
What is the minimum number of x-intercepts that a 7th degree polynomial might have?
1
What kind of polynomial is 3x3 plus x plus 1?
what kind of polynomial is shown 3x3+x+1
How do you write a polynomial function with rational coefficients in standard form with given zeros of -1 -1 1?
The polynomial is (x + 1)*(x + 1)*(x - 1) = x3 + x2 - x - 1
What is the least degree of a polynomial with the roots 3 0 -3 and 1?
The polynomial P(x)=(x-3)(x-0)(x+3)(x-1) is of the fourth degree.
What best describes the relationship between x plus 1 and the polynomial x2 minus x minus 2?
X2 - X - 2(X + 1)(X - 2)===============(X + 1) is a factor of the above polynomial.
Is x2plus x-1 a polynomial?
Yes, it is.
What is the answer to factor the following polynomial x to the second power minus one?
(x + 1)(x - 1)
Polynomial x2 plus 9x plus 8 Enter each factor as a polynomial in descending order?
(x + 8)(x + 1)
How do you factor the polynomial x2 plus 9x plus 8 with each factor as a polynomial in descending order?
(x + 8)(x + 1)
What is the second degree polynomial that creates the golden ratio?
The polynomial equation is x2 - x - 1 = 0.
What is the difference between the polynomial and multinomial?
A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication operations. It typically has one or more terms, each of which can have a different degree. A multinomial, on the other hand, is a specific type of polynomial that has more than one term with multiple variables raised to different powers. In essence, all multinomials are polynomials, but not all polynomials are multinomials.
Why the graph of a polynomial function with real coefficients must have a y-intercept but may have no x-intercept?
For a polynomial of the form y = p(x) (i.e., some polynomial function of x), having a y-intercept simply means that the polynomial is defined for x = 0 - and a polynomial is defined for any value of "x". As for the x-intercept: from left to right, a polynomial of even degree may come down, not quite reach zero, and then go back up again. A simple example is y = x2 + 1. Why is the situation for "x" and for "y" different? Well, the original equation is a polynomial in "x"; but if you solve for "x", you don't get a polynomial in "y".
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.
