Polynomials - Introduction

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Q1. What is the degree of the polynomial 4x^3 - 2x^2 + x - 7?

Solution:

The degree of a polynomial is the highest power of x. Here, the highest power is 3.

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Q2. Which expression represents the sum of the polynomials (2x^2 + 3x) and (4x^2 - x)?

Solution:

Step 1: Combine like terms: (2x^2 + 4x^2) + (3x - x) = 6x^2 + 2x.

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Q3. What are the roots of the quadratic equation x^2 - 4x - 5 = 0?

Solution:

Step 1: Factor the equation: (x - 5)(x + 1) = 0. Step 2: Set each factor to zero: x - 5 = 0 or x + 1 = 0. Step 3: Roots are x = 5 and x = -1.