USMC PiCAT Practice Test – Prep Guide and Exam Questions

To solve the expression given in the question, you need to multiply 5x by the polynomial 3x² - 5.

First, perform the multiplication of 5x with each term in the polynomial:

1. Multiply 5x by 3x²:

- This gives you 15x³ (5 times 3 equals 15, and x times x² equals x³).

2. Next, multiply 5x by -5:

- This results in -25x (5 times -5 equals -25, and the x remains).

Putting these results together, you get:

15x³ - 25x.

This aligns perfectly with the chosen answer, which is 15x³ - 25x. The key to understanding this question lies in recognizing the distributive property of multiplication over addition or subtraction in polynomials, and that was applied correctly to arrive at the correct answer.