Polynomials-philippine Grade 7 Mathematics

A polynomial that is composed of three terms is called a trinomial. A trinomial is a specific type of polynomial that consists of three monomials separated by addition or subtraction operators. The term "tri" in trinomial refers to the three terms present in the polynomial. Therefore, the correct answer is trinomial.

A binomial is a polynomial that is composed of two terms. It is a specific type of polynomial that consists of two monomials, which are expressions with a single term. The term "bi" in binomial suggests that there are two terms involved. Therefore, the given correct answer is "Binomial."

A monomial is a polynomial that is composed of only one term. This means that it does not have any addition or subtraction operations between different terms. It can be a constant, a variable, or a product of constants and variables raised to non-negative integer exponents. Therefore, the given correct answer for this question is "Monomial".

The given polynomial, 4x+10y+5xy-3x, is a multinomial because it consists of multiple terms with different variables and coefficients. It has terms with only x, only y, and a combination of x and y, making it a polynomial with more than two terms. Therefore, the correct answer is multinomial.

A polynomial is defined as an algebraic expression with one or more terms, where each term consists of a coefficient multiplied by a variable raised to a non-negative integer power. The number 1 can be considered a polynomial because it can be written as 1x^0, where the coefficient is 1 and the variable x is raised to the power of 0. Therefore, 1 satisfies the criteria of being a polynomial and the answer is true.

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The statement "Is x not a polynomial?" is asking if x is not a polynomial, which means it is asking if x is a polynomial. The correct answer is False because x is indeed a polynomial. A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division or negative exponents. Since x is a variable, it can be considered a polynomial of degree 1.

A polynomial is an algebraic expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication operations. The expression 1/x does not fit this definition since it contains a variable in the denominator, which violates the requirement of non-negative integer exponents. Therefore, 1/x is not a polynomial.

A polynomial is an algebraic expression that consists of variables raised to nonnegative integer powers, along with coefficients. It does not include any operations such as division or square roots. The given definition states that a polynomial involves only nonnegative integers powers of one or more variables, which aligns with the characteristics of a polynomial. Therefore, the correct answer is Polynomial.

The explanation for the given correct answer is that the degree of a polynomial is determined by the highest exponent of the variable included in the polynomial. By adding the exponents of the variables, we can determine the degree of the polynomial. Therefore, the statement is true.

A multinomial is a polynomial that is composed of four or more terms. It is a generalization of a binomial, which has two terms. In this case, the given answer "Multinomial" correctly describes a polynomial with four or more terms.

The given expression is a sum of three terms: -2xy+ z-1, 7xy+2z+8, and 10xy-5z-3. To find the sum, we combine like terms by adding the coefficients of the same variables. In this case, we have -2xy + 7xy + 10xy = 15xy, z - 5z = -4z, and -1 + 8 - 3 = 4. Therefore, the sum of the three terms is 15xy - 4z + 4, which matches the given answer of 15xy - 2z + 4.

The degree of a term refers to the exponent of the variable in that term. It represents the highest power to which the variable is raised. For example, in the term 3x^2, the degree is 2 because the variable x is raised to the power of 2. The degree helps determine the overall degree of a polynomial, which is the highest degree among all its terms.

In order for 2+x to be a polynomial, x must be a variable and not a specific value. A polynomial is an algebraic expression with one or more terms, and each term consists of a variable raised to a non-negative integer exponent. Therefore, x can be any real number and is not restricted to being a natural number.

The question asks whether 4 raised to c is a polynomial. The answer states that it is a polynomial if c is a natural number, as raising 4 to a natural number will result in a polynomial expression. However, if c is a negative integer, fraction, or irrational number, then 4 raised to c will not be a polynomial.