Multiply the polynomial expressions (2x^2 - 3) (x + 5).

Question

3x^2 + 7x - 15
2x^3 + 10x^2 - 3x - 15
3x^3 + 10x^2 - 3x - 15
2x^2 - 3x - 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).

Here's how we can do it step-by-step:

1. Distribute \( 2x^2 \) to both terms in \( (x + 5) \):

   • \( 2x^2 \cdot x = 2x^3 \)
   • \( 2x^2 \cdot 5 = 10x^2 \)

2. Distribute \( -3 \) to both terms in \( (x + 5) \):

   • \( -3 \cdot x = -3x \)
   • \( -3 \cdot 5 = -15 \)

3. Combine all the terms: \[ 2x^3 + 10x^2 - 3x - 15 \]

So the product \( (2x^2 - 3)(x + 5) = 2x^3 + 10x^2 - 3x - 15 \).

Among your answer choices, the correct one is:

\[ \boxed{2x^3 + 10x^2 - 3x - 15} \]