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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?
Any sum of one or more terms is called a Polynomial. Polynomials have different names. for example x is a monomial* x+1 is a binomial x-1+y is a trinomial x-1+y+2x is a multinomial (could have been called quadnomial but ... lol nah) So what is a Quadratic? It is just a polynomial where the highest exponent (power) is 2. Basically, a polynomial of the 2nd degree algebraically. For example, x²+y-3 is a quadratic trinomial x² is a quadratic monomial *by the way if you are wondering what makes a term like x or x² a sum or a polynomial when there is nothing else you see that is being added or taken away then see this ... x = x + 1 - 1 x² = x² + 1 - 1
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 a prime polynomial?
A prime polynomial is a polynomial that cannot be factored into the product of two non-constant polynomials over its coefficient field. In other words, it has no divisors other than itself and the unit (constant) polynomials. For example, in the field of real numbers, (x^2 + 1) is a prime polynomial because it cannot be factored into real linear factors. Conversely, polynomials like (x^2 - 1) are not prime because they can be factored as ((x - 1)(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.
What is type a polynomial with integer coefficients and a leading coefficient of 1 in the box below?
A polynomial with integer coefficients and a leading coefficient of 1 is called a monic polynomial. An example of such a polynomial is ( f(x) = x^3 - 4x^2 + 6x - 2 ). In this polynomial, all coefficients are integers, and the leading term ( x^3 ) has a coefficient of 1.
Is x over 3 a polynomial?
No, ( \frac{x}{3} ) is not considered a polynomial because it is expressed as a rational expression. However, if you rewrite it as ( \frac{1}{3}x ), it is a polynomial of degree 1, since it can be expressed in the standard form ( ax^n ), where ( a = \frac{1}{3} ) and ( n = 1 ). Polynomials can include constants, whole number coefficients, and non-negative integer exponents only.
What is the quotient in polynomial form?
The quotient in polynomial form refers to the result obtained when one polynomial is divided by another polynomial using polynomial long division or synthetic division. It expresses the division result as a polynomial, which may include a remainder expressed as a fraction of the divisor. The quotient can help simplify expressions and solve polynomial equations. For example, dividing (x^3 + 2x^2 + x + 1) by (x + 1) yields a quotient of (x^2 + x) with a remainder.
Is x2plus x-1 a polynomial?
Yes, it is.
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 2 -4 and 1 plus 3i?
To write a polynomial function with real coefficients given the zeros 2, -4, and (1 + 3i), we must also include the conjugate of the complex zero, which is (1 - 3i). The polynomial can be expressed as (f(x) = (x - 2)(x + 4)(x - (1 + 3i))(x - (1 - 3i))). Simplifying the complex roots, we have ((x - (1 + 3i))(x - (1 - 3i)) = (x - 1)^2 + 9). Thus, the polynomial in standard form is: [ f(x) = (x - 2)(x + 4)((x - 1)^2 + 9). ] Expanding this gives the polynomial (f(x) = (x - 2)(x + 4)(x^2 - 2x + 10)), which can be further simplified to the standard form.
What is the answer to factor the following polynomial x to the second power minus one?
(x + 1)(x - 1)
Why are polynomials not closed under division?
Polynomials are not closed under division because dividing one polynomial by another can result in a quotient that is not a polynomial. Specifically, when a polynomial is divided by another polynomial of a higher degree, the result can be a rational function, which includes terms with variables in the denominator. For example, dividing (x^2) by (x) gives (x), a polynomial, but dividing (x) by (x^2) results in (\frac{1}{x}), which is not a polynomial. Thus, the closure property does not hold for polynomial division.
