Question

expand the expression to a polynomial in standard form: (x + 2)(3x² + 5x + 10)

Explanation:

Step1: Apply the distributive property (FOIL for polynomials)

Multiply \( x \) by each term in \( 3x^2 + 5x + 10 \) and \( 2 \) by each term in \( 3x^2 + 5x + 10 \).
\( x(3x^2 + 5x + 10) + 2(3x^2 + 5x + 10) \)
\( = 3x^3 + 5x^2 + 10x + 6x^2 + 10x + 20 \)

Step2: Combine like terms

Combine the \( x^2 \) terms and the \( x \) terms.
For \( x^2 \) terms: \( 5x^2 + 6x^2 = 11x^2 \)
For \( x \) terms: \( 10x + 10x = 20x \)
So the expression becomes \( 3x^3 + 11x^2 + 20x + 20 \)

Answer:

\( 3x^3 + 11x^2 + 20x + 20 \)