Question

Multiply the polynomial expressions (2x2−3)(x+5)?

2x3+10x2−3x−15

3x3+10x2−3x−15

2x2−3x−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).

Let's go step by step:

1. Distribute \( 2x^2 \) to both \( x \) and \( 5 \):
\[
2x^2 \cdot x = 2x^3
\]
\[
2x^2 \cdot 5 = 10x^2
\]

2. Distribute \( -3 \) to both \( x \) and \( 5 \):
\[
-3 \cdot x = -3x
\]
\[
-3 \cdot 5 = -15
\]

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

Thus, the final result of multiplying \( (2x^2 - 3)(x + 5) \) is:
\[
\boxed{2x^3 + 10x^2 - 3x - 15}
\]

From the options given, the correct answer is:
\( 2x^3 + 10x^2 - 3x - 15 \).