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The first term of a polynomial is the term with the highest degree, typically written in standard form. For example, in the polynomial (3x^4 + 2x^3 - x + 5), the first term is (3x^4). If a polynomial has multiple terms, the first term is determined by the term with the largest exponent of the variable. If the polynomial is expressed in descending order, the first term is simply the first term listed.
What else can I help you with?
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.
Explain how you multiply two polynomials?
To multiply two polynomials, you apply the distributive property, also known as the FOIL method for binomials. Each term in the first polynomial is multiplied by each term in the second polynomial. After performing all the multiplications, you combine like terms to simplify the resulting polynomial. Finally, ensure that the polynomial is written in standard form, with terms ordered by decreasing degree.
How can you tell if a polynomial is a perfect square?
Let's take a quadratic polynomial. There are three terms in a quadratic polynomial. Example: X^2 + 8X + 16 = 0 To satisfy the criteria of a perfect square polynomial, the first and last term of the polynomial must be squares. The middle term must be either plus or minus two multiplied by the square root of the first term multiplied by the square root of the last term. If these three criteria are satisifed, the polynomial is a perfect square. Let us take the above quadratic. X^2 + 8X + 16 = X^2 + 2(4X) + 4^2 = (X+4)^2 As we can see, each criteria is satified and the polynomial does indeed form a perfect square.
What is the name of polynomial with 6 terms?
A polynomial with six terms is commonly referred to as a "hexomial." The term "hexomial" comes from the prefix "hexa-" meaning six, indicating the number of terms present in the polynomial. Each term in a hexomial can have varying degrees and coefficients, contributing to the overall structure of the polynomial.
What is (9x2 10x 4) (9x2 5x 1?
To multiply the polynomials ( (9x^2 + 10x + 4) ) and ( (9x^2 + 5x + 1) ), you can use the distributive property (also known as the FOIL method for binomials). Multiply each term in the first polynomial by each term in the second polynomial, then combine like terms. The resulting polynomial will be a degree 4 polynomial. For the full expansion, the result is ( 81x^4 + 85x^3 + 49x^2 + 20x + 4 ).
How do you multiply monomial by a polynomial?
you foil it out.... for example take the first number or variable of the monomial and multiply it by everything in the polynomial...
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.
How do explain how to multiply polynomials?
You simply need to multiply EACH term in one polynomial by EACH term in the other polynomial, and add everything together.
How do you find the degree of polynomials?
First look at the degree of each term: this is the power of the variable. The highest such number, from all the terms in the polynomial is the degree of the polynomial. Thus x2 + 1/7*x + 3 has degree 2. x + 7 - 2x3 + 0.8x5 has degree 5.
How can you know that a term is polynomial?
A [single] term cannot be polynomial.
How can you tell if a polynomial is a perfect square?
Let's take a quadratic polynomial. There are three terms in a quadratic polynomial. Example: X^2 + 8X + 16 = 0 To satisfy the criteria of a perfect square polynomial, the first and last term of the polynomial must be squares. The middle term must be either plus or minus two multiplied by the square root of the first term multiplied by the square root of the last term. If these three criteria are satisifed, the polynomial is a perfect square. Let us take the above quadratic. X^2 + 8X + 16 = X^2 + 2(4X) + 4^2 = (X+4)^2 As we can see, each criteria is satified and the polynomial does indeed form a perfect square.
What is the definition of degree of the polynomial?
The degree of a polynomial is the highest degree of its terms.The degree of a term is the sum of the exponents of the variables.7x3y2 + 15xy6 + 23x2y2The degree of the first term is 5.The degree of the second term is 7.The degree of the third term is 4.The degree of the polynomial is 7.
How can you find a degree in a polynomial?
The degree of a polynomial is the highest degree of its terms. The degree of a term is the sum of the exponents of the variables that appear in it.7x2y2 + 4x2 + 5y + 13 is a polynomial with four terms. The first term has a degree of 4, the second term has a degree of 2, the third term has a degree of 1 and the fourth term has a degree of 0. The polynomial has a degree of 4.
What is the name of polynomial with 6 terms?
A polynomial with six terms is commonly referred to as a "hexomial." The term "hexomial" comes from the prefix "hexa-" meaning six, indicating the number of terms present in the polynomial. Each term in a hexomial can have varying degrees and coefficients, contributing to the overall structure of the polynomial.
Degree of a terms of polynomial?
The degree of a polynomial is the highest degree of its terms. The degree of a term is the sum of the exponents of the variables that appear in it.For example, the polynomial 8x2y3 + 5x - 10 has three terms. The first term has a degree of 5, the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial is degree five.
What is (9x2 10x 4) (9x2 5x 1?
To multiply the polynomials ( (9x^2 + 10x + 4) ) and ( (9x^2 + 5x + 1) ), you can use the distributive property (also known as the FOIL method for binomials). Multiply each term in the first polynomial by each term in the second polynomial, then combine like terms. The resulting polynomial will be a degree 4 polynomial. For the full expansion, the result is ( 81x^4 + 85x^3 + 49x^2 + 20x + 4 ).
Do you use the distributive property with a monomial and a polynomial?
If you want to multiply the monomial by the polynomial, yes. In that case, you have to multiply the monomial by every term of the polynomial. For example: a (b + c + d) = ab + ac + ad More generally, when you multiply together two polynomials, you have to multiply each term in one polynomial by each term of the other polynomial; for example: (a + b)(c + d) = ac + ad + bc + bd All this can be derived from the distributive property (just apply the distributive property repeatedly).
