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What property of polynomial multiplication says that the product of two polynomials is always a polynomial?
Clouser
Which property of polynomial multiplication says that the product of two polynomials is always a polynomial?
That property is called CLOSURE.
Sum and product of the zeros of a quadratic polynomial are -12 and -3 respectively what is the quadratic polynomial?
x2 + 15x +36
How can you get the special product of a trinomial?
You represent a generic trinomial with some letters, then just carry out the desired operations. The general rule to multiply polynomials is that each term in one polynomial must be multiplied by each term in the other polynomial. For example, to multiply a trinomial by itself - i.e., square it - you get: (a + b + c) (a + b + c) = a2 + ab + ac + ab + b2 + bc + ac + bc + c2 Next, you can group similar terms; well, I'll leave that to you.
How do you solve a cubic equation?
If you can find a simple factoring of the cubic polynomial, then it is fairly easy to solve (by the zero-product property). Otherwise it isn't; there are several iterative methods, but none of them is simple. That's why the solution of polynomials of degree is usually not covered in high school, or even in college. If you are really interested in the more or less complicated details, the Wikipedia article on "Root-finding algorithm" gives you an introduction.
Will the product of two polynomials always be a polynomial?
Yes, the product of two polynomials will always be a polynomial. This is because when you multiply two polynomials, you are essentially combining like terms and following the rules of polynomial multiplication, which results in a new polynomial with coefficients that are the products of the corresponding terms in the original polynomials. Therefore, the product of two polynomials will always be a polynomial.
Is the product of two polynomials always a polynomial?
Yes. A polynomial multiplying by a polynomial will always have a multi-termed product. Hope this helps!
What property of polynomial multiplication says that the product of two polynomials is always a polynomial?
Clouser
What is a polynomial that cannot be written as a product of two polynomials?
prime
Which property of polynomial multiplication says that the product of two polynomials is always a polynomial?
That property is called CLOSURE.
To find the product of two polynomials multiply the top polynomial by each of the bottom polynomial?
(b+8)(b+8)
When polynomial is a quadratic polynomial?
Whenever there are polynomials of the form aX2+bX+c=0 then this type of equation is know as a quadratic equation. to solve these we usually break b into two parts such that there product is equal to a*c and I hope you know how to factor polynomials.
What is the answer called when 2 or more polynomials are multipiled?
A polynomial is any number of the form Ax^n + Bx^n-1 + ... + c. So, multiplying numbers with exponents with any other numbers with exponents in polynomials only results in another, larger polynomial. Since this is multiplication, you could call the resultant polynomial a product.
What are the 5 properties of polynomials?
A sum of polynomials is a polynomial.A product of polynomials is a polynomial.A composition of two polynomials is a polynomial, which is obtained by substituting a variable of the first polynomial by the second polynomial.The derivative of the polynomial anxn + an-1xn-1 + ... + a2x2 + a1x + a0 is the polynomial nanxn-1 + (n-1)an-1xn-2 + ... + 2a2x + a1. If the set of the coefficients does not contain the integers (for example if the coefficients are integers modulo some prime number p), then kak should be interpreted as the sum of ak with itself, k times. For example, over the integers modulo p, the derivative of the polynomial xp+1 is the polynomial 0.If the division by integers is allowed in the set of coefficients, a primitive or antiderivative of the polynomial anxn + an-1xn-1 + ... + a2x2 + a1x + a0 is anxn+1/(n+1) + an-1xn/n + ... + a2x3/3 + a1x2/2 + a0x +c, where c is an arbitrary constant. Thus x2+1 is a polynomial with integer coefficients whose primitives are not polynomials over the integers. If this polynomial is viewed as a polynomial over the integers modulo 3 it has no primitive at all.
What is a polynomial term?
A polynomial term is a product of a number and one or more variables raised to various powers. The powers must be non-negative integers.
When is an algebraic expression considered as polynomial?
A polynomial is really an algebraic expression that consists of two or more monomials. A monomial is a number, a variable, or a product of a number with non-negative exponents. Some examples of polynomials are: 2x+3y-1;3bc+7cd-y;7mny-my+n To be exact, polynomials is any expression with the lowest power of unknown as 0 or more. 6z+5, 5x4+9x-1 are some examples of polynomials. However, if the unknown is in the denominator, it is not a polynomial. Also, if the expression has a negative power like 3-2, it will become a fraction when you remove the negative sign (3-2 = 1/32).-42 is a polynomial because it is also -42x0 except that people do not need to write the x0 since x0 = 1 and when you multiply -42x0, it still ends up becoming -42.
How can you factor a polynomial in standard form completely?
You can factor a polynomial using one of these steps: 1. Factor out the greatest common monomial factor. 2. Look for a difference of two squares or a perfect square trinomial. 3. Factor polynomials in the form ax^2+bx+c into a product of binomials. 4. Factor a polynomial with 4 terms by grouping.
