Question

12x⁴ + 13x³ + 3x²

Explanation:

Step1: Factor out common term

$12x^4 +13x^3 +3x^2 = x^2(12x^2 +13x +3)$

Step2: Factor quadratic trinomial

Find two numbers that multiply to $12\times3=36$ and add to $13$: $9$ and $4$.
Split and factor:
$12x^2 +13x +3 = 12x^2 +9x +4x +3 = 3x(4x+3) +1(4x+3) = (3x+1)(4x+3)$

Step3: Combine factors

$x^2(3x+1)(4x+3)$

Answer:

$x^2(3x+1)(4x+3)$