Polynomials - Introduction

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Q1. What is the product of the factors (x + 2) and (x - 3)?

Solution:

Step 1: Use the distributive property: x^2 - 3x + 2x - 6 = x^2 - x - 6.

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Q2. What is the product of the roots of the polynomial x^2 - 4x + 3?

Solution:

The product of the roots is given by c/a. Here, c = 3, so the product is 3.

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Q3. What is the result of factoring the expression x^2 + 7x + 10?

Solution:

Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Factor: (x + 5)(x + 2).

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Q4. Which expression represents the sum of the polynomials (3x^2 + 2x) and (4x^2 - 5x)?

Solution:

Step 1: Combine like terms: (3x^2 + 4x^2) + (2x - 5x) = 7x^2 - 3x.