Multiply the polynomial expressions (2x2−3)(x+5)?

Question

2x3+10x2−3x−15

3x3+10x2−3x−15

2x2−3x−15

3x2+7x−15

Answer 1

To multiply the polynomial expressions \( (2x^2 - 3)(x + 5) \), we can use the distributive property (also known as the FOIL method for binomials).

Let's go step by step:

1. Distribute \( 2x^2 \) to both \( x \) and \( 5 \): \[ 2x^2 \cdot x = 2x^3 \] \[ 2x^2 \cdot 5 = 10x^2 \]

2. Distribute \( -3 \) to both \( x \) and \( 5 \): \[ -3 \cdot x = -3x \] \[ -3 \cdot 5 = -15 \]

3. Now combine all these results: \[ 2x^3 + 10x^2 - 3x - 15 \]

Thus, the final result of multiplying \( (2x^2 - 3)(x + 5) \) is: \[ \boxed{2x^3 + 10x^2 - 3x - 15} \]

From the options given, the correct answer is: \( 2x^3 + 10x^2 - 3x - 15 \).