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 - no response given

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

3x2+7x−15
3 x squared plus 7 x minus 15 - no response given

2x2−3x−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).

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 \( (x + 5) \):

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

Now combine all the terms we obtained: \[ 2x^3 + 10x^2 - 3x - 15 \]

So, the simplified result is: \[ 2x^3 + 10x^2 - 3x - 15 \]

Therefore, the correct response is: 2x^3 + 10x^2 - 3x - 15.