Multiply the polynomial expressions (2x2−3)(x+5) .(1 point)

Question

Responses

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

2x3+10x2−3x−15
2 x cubed plus 10 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. Multiply \( 2x^2 \) by \( x \): \[ 2x^2 \cdot x = 2x^3 \]

2. Multiply \( 2x^2 \) by \( 5 \): \[ 2x^2 \cdot 5 = 10x^2 \]

3. Multiply \( -3 \) by \( x \): \[ -3 \cdot x = -3x \]

4. Multiply \( -3 \) by \( 5 \): \[ -3 \cdot 5 = -15 \]

Now, combine all these results: \[ 2x^3 + 10x^2 - 3x - 15 \]

Therefore, the correct answer is: 2x³ + 10x² - 3x - 15.