Question

what is the product of (2x + 1)(x² + 2x - 8)?

Explanation:

Step1: Apply distributive property (FOIL extended)

Multiply each term in the first polynomial by each term in the second polynomial:
$(2x + 1)(x^2 + 2x - 8) = 2x(x^2) + 2x(2x) + 2x(-8) + 1(x^2) + 1(2x) + 1(-8)$

Step2: Simplify each term

Calculate each product:
$2x \cdot x^2 = 2x^3$,
$2x \cdot 2x = 4x^2$,
$2x \cdot (-8) = -16x$,
$1 \cdot x^2 = x^2$,
$1 \cdot 2x = 2x$,
$1 \cdot (-8) = -8$

Step3: Combine like terms

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

• \(x^3\) term: \(2x^3\)
• \(x^2\) terms: \(4x^2 + x^2 = 5x^2\)
• \(x\) terms: \(-16x + 2x = -14x\)
• Constant term: \(-8\)

So the product is \(2x^3 + 5x^2 - 14x - 8\).

Answer:

\(2x^3 + 5x^2 - 14x - 8\)