0
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.
Still curious? Ask our experts.
Chat with our AI personalities
Fran
Coach
TaigaAdd your answer:
Earn +20 pts
Is 4 - 3x plus 5x2 a polynomial?
Yes. If you add, subtract or multiply (but not if you divide) any two polynomials, you will get a polynomial.
How do you multiply three or more polynomials?
To multiply TWO polynomials, you multiply each term in the first, by each term in the second. This can be justified by a repeated application of the distributive law. Two multiply more than two polynomials, you multiply the first two. Then you multiply the result with the third polynomial. If there are any more, multiply the result with the fourth polynomial, etc. Actually the polynomials can be multiplied in any order; both the communitative and associate laws apply.
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.
Is x2 plus 27 a polynomial?
Yes, although we generally refer to polynomials with two terms, like this one, as binomials.
Multiply the two polynomials by distributing (x2 3x plus 2)(x plus 2)?
The idea here is to multiply each term in the first polynomial by each term in the second polynomial.
