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

Question

.(1 point)
Responses

2x^3+10x2−3x−15
2 x cubed plus 10 x squared minus 3 x minus 15 - no response given

2x^2−3x−15
2 x squared minus 3 x minus 15 - incorrect

3x^2+7x−15
3 x squared plus 7 x minus 15 - no response given

3x^3+10x2−3x−15

Answer 1

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

Here’s the breakdown of the multiplication:

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

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

2. Distribute \(-3\):

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

Now, we combine all the results:

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

Thus, the final answer is:

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

So the correct response is:

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