To find the quotient of the given expression, we first need to clarify what we’re dividing. If we have the expression 2x² ÷ (10x ÷ (12 ÷ 3)), we can simplify it step-by-step.
First, let’s simplify the innermost division: 12 ÷ 3 = 4. Now, our expression looks like this: 2x² ÷ (10x ÷ 4).
Next, we simplify the next division: 10x ÷ 4 = 2.5x. Therefore, the expression now reads: 2x² ÷ 2.5x.
Now, dividing 2x² by 2.5x can be rewritten as:
2 ÷ 2.5 * x² ÷ x = 0.8 * x = 0.8x.
So, the final quotient of the expression is 0.8x.
This result shows that when dividing the polynomial terms, we simplify the coefficients and reduce the variable terms through division, leading to a simpler expression.