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

3x2+7x−15
3 x squared plus 7 x minus 15

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

2x2−3x−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).

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

So the final answer is: \[ \boxed{2x^3 + 10x^2 - 3x - 15} \]