Degree Of Polynomial

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2. 9) 0.1h

The given expression is 0.1h. It represents a decimal number (0.1) multiplied by a variable (h). When any number is multiplied by 1, the result is the number itself. Therefore, when 0.1 is multiplied by 1, the answer is 0.1. Hence, the correct answer is 1.

Explanation

The given expression is 0.1h. It represents a decimal number (0.1) multiplied by a variable (h). When any number is multiplied by 1, the result is the number itself. Therefore, when 0.1 is multiplied by 1, the answer is 0.1. Hence, the correct answer is 1.

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3. I. State the degree in each of the following polynomials.

1) 2 - 5x

The degree of a polynomial is the highest power of the variable in the polynomial. In the given polynomial 2 - 5x, the highest power of x is 1, since it is raised to the power of 1. Therefore, the degree of the polynomial is 1.

Explanation

The degree of a polynomial is the highest power of the variable in the polynomial. In the given polynomial 2 - 5x, the highest power of x is 1, since it is raised to the power of 1. Therefore, the degree of the polynomial is 1.

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4. 6) 3/4x

The given expression is 3/4x. It can be simplified as (3/4) * x, which means multiplying 3/4 with x. When any number is multiplied by 1, the result is always the number itself. Therefore, when x is multiplied by 1, the answer will be x.

Explanation

The given expression is 3/4x. It can be simplified as (3/4) * x, which means multiplying 3/4 with x. When any number is multiplied by 1, the result is always the number itself. Therefore, when x is multiplied by 1, the answer will be x.

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5. 2) 4y + 3y³ - 2y² + 5

The given expression is a polynomial with three terms: 4y, 3y^3, and -2y^2. When divided by 3, each term is divided by 3 individually. The result of dividing 4y by 3 is (4/3)y. The result of dividing 3y^3 by 3 is y^3. The result of dividing -2y^2 by 3 is (-2/3)y^2. Finally, the constant term 5 is also divided by 3, resulting in (5/3). Therefore, the expression simplifies to (4/3)y + y^3 - (2/3)y^2 + (5/3), which is the answer.

Explanation

The given expression is a polynomial with three terms: 4y, 3y^3, and -2y^2. When divided by 3, each term is divided by 3 individually. The result of dividing 4y by 3 is (4/3)y. The result of dividing 3y^3 by 3 is y^3. The result of dividing -2y^2 by 3 is (-2/3)y^2. Finally, the constant term 5 is also divided by 3, resulting in (5/3). Therefore, the expression simplifies to (4/3)y + y^3 - (2/3)y^2 + (5/3), which is the answer.

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6. 10) 5x³y⁴ + 10x⁴y⁵

The given expression is a polynomial consisting of two terms. The first term, 5x3y4, has a degree of 7 (3+4) and the second term, 10x4y5, has a degree of 9 (4+5). Since the expression is being divided by 9, we can simplify it by dividing each term by 9. Therefore, the answer is 9.

Explanation

The given expression is a polynomial consisting of two terms. The first term, 5x3y4, has a degree of 7 (3+4) and the second term, 10x4y5, has a degree of 9 (4+5). Since the expression is being divided by 9, we can simplify it by dividing each term by 9. Therefore, the answer is 9.

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8. 5) 2x + 5x³y + 2x²y³ - 5y

The given expression is a polynomial with terms involving variables x and y. When we divide this polynomial by 5, each term is divided by 5. Since the constant term -5y is divisible by 5, the result is 5.

Explanation

The given expression is a polynomial with terms involving variables x and y. When we divide this polynomial by 5, each term is divided by 5. Since the constant term -5y is divisible by 5, the result is 5.

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