Question 3 of 49beginner✨ CreateShort Answer3 marks

Write polynomials of degrees 1, 2 and 3.

Correct Answer

A polynomial of degree 1 is known as a linear polynomial. An example from the text is 3z+73z + 7, where the highest power of the variable zz is 1. A polynomial of degree 2 is referred to as a quadratic polynomial. An example is x2+5x+1x^2 + 5x + 1, where the highest power of the variable xx is 2. A polynomial of degree 3 is called a cubic polynomial. An example is 5y3+y2+2y−15y^3 + y^2 + 2y - 1, where the highest power of the variable yy is 3.

Exercise: EXERCISE SET 2.1 | Q: 2 | (Page 3)
For More Understanding

Explanation

The question asks for examples of polynomials with degrees 1, 2, and 3. The textbook context defines the degree of a polynomial as the highest power of the variable. It explicitly provides examples for each category: degree 1 (linear polynomial) as 3z + 7, degree 2 (quadratic polynomial) as x2x^{2} + 5x + 1, and degree 3 (cubic polynomial) as 5y35y^{3} + y2y^{2} + 2y - 1.

Solution Steps

  1. Step 1: Identify a polynomial of degree 1 (linear polynomial), e.g., 3z+73z + 7.

  2. Step 2: Identify a polynomial of degree 2 (quadratic polynomial), e.g., x2+5x+1x^2 + 5x + 1.

  3. Step 3: Identify a polynomial of degree 3 (cubic polynomial), e.g., 5y3+y2+2y−15y^3 + y^2 + 2y - 1.

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