True or False?
1. The product of 2 linear polynomials is quadratic
2. The sum of two cubic polynomials cannot have a degree greater than 3.
3. The sum of two cubic polynomials may have a degree less than 3.
4. The sum of a cubic and a quartic polynomial may have a degree different from 4.
5. The product of two monomials is a monomial.
6. The product of two binomials is a binomial.
I got:
1.T
2. T
3. F
4.F
5.F
6.T
Is this right?
I think 6th is false...bcoz in product degree is added .and binomial has degree 2... and 2+2 is 4...............
Let's go through each statement one by one:
1. The product of 2 linear polynomials is quadratic.
To determine the degree of the product of two polynomials, we need to multiply the highest degrees of each polynomial. Since linear polynomials have a degree of 1, when we multiply them, the highest degree we can get is 1 + 1 = 2. So, the statement is True.
2. The sum of two cubic polynomials cannot have a degree greater than 3.
The degree of a polynomial is determined by the highest power of the variable that appears. For two cubic polynomials, the highest degree is 3. When we add them, the resulting polynomial's degree will still be 3 or less. So, the statement is True.
3. The sum of two cubic polynomials may have a degree less than 3.
Similar to the previous explanation, the sum of two cubic polynomials will have a degree of 3 because the highest degree term in each polynomial is 3. Therefore, the statement is False.
4. The sum of a cubic and a quartic polynomial may have a degree different from 4.
When we add a cubic polynomial (degree 3) and a quartic polynomial (degree 4), the resulting polynomial's degree can be either 3 or 4, depending on the coefficients of the terms. Therefore, the statement is True.
5. The product of two monomials is a monomial.
A monomial is a polynomial with only one term. When we multiply two monomials, we multiply their coefficients together and combine the variables by adding their exponents. The resulting expression might have multiple terms if the variables have different exponents, so the statement is False.
6. The product of two binomials is a binomial.
A binomial is a polynomial with two terms. When we multiply two binomials using the distributive property, we get four terms. However, when we combine like terms, the resulting expression will have only two terms, making it a binomial. Therefore, the statement is True.
Based on these explanations:
1. True
2. True
3. False
4. True
5. False
6. True
Your answers are correct!