Question

determine the resulting polynomial:
$f(x) = 2x + 6$
$g(x) = 6x^2 - x + 10$
find: $f(x) \cdot g(x)$
answer
attempt 1 out of 2

Explanation:

Step1: Apply distributive property

Multiply each term in \( f(x) \) by each term in \( g(x) \):
\( (2x + 6)(6x^2 - x + 10) = 2x(6x^2 - x + 10) + 6(6x^2 - x + 10) \)

Step2: Distribute further

For \( 2x(6x^2 - x + 10) \):
\( 2x \cdot 6x^2 = 12x^3 \), \( 2x \cdot (-x) = -2x^2 \), \( 2x \cdot 10 = 20x \)
For \( 6(6x^2 - x + 10) \):
\( 6 \cdot 6x^2 = 36x^2 \), \( 6 \cdot (-x) = -6x \), \( 6 \cdot 10 = 60 \)

Step3: Combine like terms

Combine the \( x^2 \) terms: \( -2x^2 + 36x^2 = 34x^2 \)
Combine the \( x \) terms: \( 20x - 6x = 14x \)

Step4: Write the polynomial

Combine all terms: \( 12x^3 + 34x^2 + 14x + 60 \)

Answer:

\( 12x^3 + 34x^2 + 14x + 60 \)