Question

what is the leading coefficient of the product of the following expression.
2(x + 3)(5x − 1)(4 − x + 2x²)

10
20
30
40

Explanation:

Step1: Identify leading terms

For each polynomial factor, find the leading term (highest degree term):

• \(2\) (constant, degree 0, leading term \(2\))
• \((x + 3)\): leading term \(x\) (degree 1)
• \((5x - 1)\): leading term \(5x\) (degree 1)
• \((4 - x + 2x^2)\): leading term \(2x^2\) (degree 2)

Step2: Multiply leading terms

Multiply the leading terms of all factors:
\(2 \times x \times 5x \times 2x^2\)

First, multiply the coefficients: \(2 \times 5 \times 2 = 20\)
Then, multiply the variables: \(x \times x \times x^2 = x^{1 + 1 + 2} = x^4\)

The product of the leading terms is \(20x^4\), so the leading coefficient is \(20\).

Answer:

20