Question

find the binomial that completes the factorization.
$3x^4 + 3x = 3x(\square)(x^2 - x + 1)$

Explanation:

+1. Yes, correct blank is x+1.

Wait correction step: Step1: Factor left side: 3x⁴+3x=3x(x³ +1). Step2: Factor x³+1 as sum of cubes: x³+1³=(x+1)(x² -x +1). Step3: Substitute back: 3x(x+1)(x² -x +1). So blank is x+1.

Final Answer: $x + 1$

Step1: Factor left side monomial

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

Step2: Factor sum of cubes $x^3 +1$

$x^3 +1 = (x + 1)(x^2 - x + 1)$

Step3: Identify the binomial

Compare with right side: the blank is $x + 1$

Answer:

$x + 1$