Question

1. an expression is shown.

(8x - 5)(3x + 2x² - 6)
show the product written in standard form.

Explanation:

Step1: Apply Distributive Property

Multiply each term in the first polynomial by each term in the second polynomial:

$$
LATEXBLOCK0
$$

Step2: Combine Like Terms

Combine the terms with the same power of \(x\):

• For \(x^3\): \(16x^3\)
• For \(x^2\): \(24x^2 - 10x^2 = 14x^2\)
• For \(x\): \(-48x - 15x = -63x\)
• Constant term: \(30\)

So the polynomial in standard form (descending powers of \(x\)) is:

$$16x^3 + 14x^2 - 63x + 30$$

Answer:

\(16x^3 + 14x^2 - 63x + 30\)