Multiplying Polynomials Quick Check

Answer 1

Sure! Here’s a quick check on multiplying polynomials. Below are a few problems you can solve, followed by the answers.

Problems

1. Multiply: \( (2x + 3)(x + 4) \)

2. Multiply: \( (x - 5)(x + 2) \)

3. Multiply: \( (3x^2 + 2x)(x - 1) \)

4. Multiply: \( (x + 1)(x^2 - x + 4) \)

5. Multiply: \( (2x^3)(3x^2 - x + 5) \)

Answers

1. \( (2x + 3)(x + 4) = 2x^2 + 8x + 3x + 12 = 2x^2 + 11x + 12 \)

2. \( (x - 5)(x + 2) = x^2 + 2x - 5x - 10 = x^2 - 3x - 10 \)

3. \( (3x^2 + 2x)(x - 1) = 3x^3 - 3x^2 + 2x^2 - 2x = 3x^3 - x^2 - 2x \)

4. \( (x + 1)(x^2 - x + 4) = x^3 - x^2 + 4x + x^2 - x + 4 = x^3 + 3x + 4 \)

5. \( (2x^3)(3x^2 - x + 5) = 6x^5 - 2x^4 + 10x^3 \)

Feel free to ask if you need further explanations or additional problems!