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

Question

.(1 point)
Responses

2x3+10x2−3x−15
2 x cubed plus 10 x squared minus 3 x minus 15

3x3+10x2−3x−15
3 x cubed plus 10 x squared minus 3 x minus 15

2x2−3x−15
2 x squared minus 3 x minus 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).

1. Distributing \( 2x^2 \):

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

2. Distributing \( -3 \):

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

Now, we combine all these terms:

\[ 2x^3 + 10x^2 - 3x - 15 \]

Therefore, the result of multiplying the two polynomial expressions is:

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