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What does polynomials mean in mathematical terms?
It means the sum of several monomials.
Are all polynomials either even or odd?
No. Polynomials are made up of several terms. The terms can be even or odd (assuming they aren't variables, in which case, you don't know if they're even or odd), but the polynomial itself isn't one or the other.
How does Factoring undoes the distributive property?
when you distribute something you are adding one or more term to the other seval term so when you factor it does the opposite. Instead of giving , factoring removes one or more terms from the other several terms.
Are polynomial and trinomial the same?
A trinomial is a polynomial. All trinomials are polynomials but the opposite is not true. a trinomial= three unlike terms. a polynomial= "many" unlike terms.
How is multiplying polynomials different from adding them?
When you add polynomials, you combine only like terms together. For example, (x^3+x^2)+(2x^2+x)= x^3+(1+2)x^2+x=x^3+3x^2+x When you multiply polynomials, you multiply all pairs of terms together. (x^2+x)(x^3+x)=(x^2)(x^3)+(x^2)(x)+(x)(x^3)+(x)(x)=x^5+x^3+x^4+x^2 Basically, in addition you look at like terms to simplify. In multiplication, you multiply each term individually with every term on the opposite side, ignoring like terms.
How do multiplying and factoring polynomials compare?
Multiplying polynomials involves distributing each term of one polynomial to every term of another, combining like terms to simplify the result. In contrast, factoring polynomials is the process of expressing a polynomial as a product of simpler polynomials or monomials. While multiplication expands expressions, factoring seeks to reverse that process by finding the original components. Both operations are fundamental in algebra and are often interconnected; for instance, factoring can be used to simplify the process of multiplication by breaking down complex polynomials.
What are the laws of factoring polynomials?
The laws of factoring polynomials include several key principles: First, identify common factors among terms to factor them out. Second, apply special factoring techniques, such as the difference of squares, perfect square trinomials, and the sum or difference of cubes. Third, use the quadratic formula or factoring by grouping for polynomials of higher degrees. Lastly, always check for irreducibility, ensuring the polynomial is factored completely.
What is another name for factoring by grouping?
Another name for factoring by grouping is the "method of grouping." This technique involves rearranging and grouping terms in a polynomial to factor it into a product of simpler expressions. It is particularly useful for polynomials with four or more terms.
What does factoring a polynomial mean?
It means finding numbers (constant terms), or polynomials of the same or smaller order that multiply together to give the original polynomial.
Hellllp meee. How do you add polynomials when you don't have any like terms?
Hellllp meee, how do you add polynomials when you don't have any like terms is a very common questions when it comes to this type of math. However, the polynomials can only be added if all terms are alike. No unlike terms can be added within the polynomials.
How many terms does polynomials have?
3
What are the operation of polynomials?
Adding and subtracting polynomials is simply the adding and subtracting of their like terms.
What are the rules in addition of polynomials?
Add together the coefficients of "like" terms. Like terms are those that have the same powers of the variables in the polynomials.
What is the distributive property when multiplying polynomials?
You just multiply the term to the polynomials and you combine lije 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.
Polynomials are written with the exponents of the terms in order?
descending
Rules in adding polynomials?
To add polynomials , simply combine similar terms. Combine similar terms get the sum of the numerical coefficients and affix the same literal coefficient .
