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

Question

.(1 point)
Responses

A) 2x^3+10x^2−3x−15
2 x cubed plus 10 x squared minus 3 x minus 15

B) 3x^2+7x−15
3 x squared plus 7 x minus 15

C) 2x^2−3x−15
2 x squared minus 3 x minus 15

D) 3x^3+10x^2−3x−15
3 x cubed plus 10 x squared minus 3 x minus 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):

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 these results: \[ 2x^3 + 10x^2 - 3x - 15 \]

The correct answer is: A) \( 2x^3 + 10x^2 - 3x - 15 \).