Question

(5x+2)(x²-3x+6)
5x³ - 13x² + 24x +12
5x³ + 17x² - 24x +12
5x³ - 17x² +24x +12
5x³ +13x² - 24x - 12

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \(5x\) by each term in \((x^2 - 3x + 6)\) and \(2\) by each term in \((x^2 - 3x + 6)\):
\(5x \cdot x^2 = 5x^3\), \(5x \cdot (-3x) = -15x^2\), \(5x \cdot 6 = 30x\)
\(2 \cdot x^2 = 2x^2\), \(2 \cdot (-3x) = -6x\), \(2 \cdot 6 = 12\)

Step2: Combine like terms

For \(x^3\): \(5x^3\)
For \(x^2\): \(-15x^2 + 2x^2 = -13x^2\)
For \(x\): \(30x - 6x = 24x\)
Constant term: \(12\)

So the expanded form is \(5x^3 - 13x^2 + 24x + 12\)

Answer:

\(5x^3 - 13x^2 + 24x + 12\) (matching the first option, assuming the first option is \(5x^3 - 13x^2 + 24x + 12\))