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What is the step of factorising by grouping?
Factorising by grouping involves rearranging and grouping terms in a polynomial to factor out common factors. First, you split the polynomial into two groups, then factor out the greatest common factor from each group. If done correctly, these groups will have a common binomial factor, which can then be factored out, resulting in a simplified expression. This method is particularly useful for polynomials with four terms.
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.
Can the sum of three polynomials again be a polynomial?
The sum of two polynomials is always a polynomial. Therefore, it follows that the sum of more than two polynomials is also a polynomial.
What do you call this quantity by polynomials with 2 terms?
Polynomials with two terms are called "binomials." A binomial consists of two monomial terms separated by either a plus or minus sign. For example, expressions like (3x + 5) or (2y^2 - 4) are both binomials.
Give examples of some kinds of polynomials?
Binomials and trinomials are two types of polynomials. The first has two terms and the second has three.
Which property of polynomial subtraction says that the difference of two polynomials is always a polynomial?
The property that states the difference of two polynomials is always a polynomial is known as the closure property of polynomials. This property indicates that when you subtract one polynomial from another, the result remains within the set of polynomials. This is because polynomial operations (addition, subtraction, and multiplication) preserve the degree and structure of polynomials. Thus, the difference of any two polynomials will also be a polynomial.
What property of polynomial subtraction says that the difference of two polynomials is always a polynomial?
The property of polynomial subtraction that ensures the difference of two polynomials is always a polynomial is known as closure under subtraction. This property states that if you take any two polynomials, their difference will also yield a polynomial. This is because subtracting polynomials involves combining like terms, which results in a polynomial expression that adheres to the same structure as the original polynomials.
What has the author T H Koornwinder written?
T. H. Koornwinder has written: 'Jacobi polynomials and their two-variable analysis' -- subject(s): Jacobi polynomials, Orthogonal polynomials
Are polynomials closed under the operations of subtraction addition and multiplication?
Yes, polynomials are closed under the operations of addition, subtraction, and multiplication. This means that when you add, subtract, or multiply two polynomials, the result is always another polynomial. For example, if ( p(x) ) and ( q(x) ) are polynomials, then ( p(x) + q(x) ), ( p(x) - q(x) ), and ( p(x) \cdot q(x) ) are all polynomials as well. However, polynomials are not closed under division, as dividing one polynomial by another can result in a non-polynomial expression.
How do you factorise 15x-27xy?
Factorising 15x-27xy gives 3x (5 - 9y).Factorising is to express a number or expression as a product of factors.When factorising always look for common factors. To factorise (15x-27xy) look for the highest factor between the two terms (3x). 15x - 27y = 3x (5 - 9y)
Are polynomials a closed set under addition?
Yes, polynomials are a closed set under addition. This means that if you take any two polynomials and add them together, the result will also be a polynomial. The sum of two polynomials retains the structure of a polynomial, as it still consists of terms with non-negative integer exponents and real (or complex) coefficients.
How do you count terms in polynomials?
Terms in polynomials are simply separated by a plus or minus sign. For example, if you had: x+12x, that would be a binomial (two terms). A trinomial is when the expression has three or more terms, 7x+12x-6x.
