3. $$ 4 x^{4}-12 x^{3}+8 x^{2} $$

Question

UpStudy AI · Accepted Answer

Let's factor the expression 4x⁴ - 12x³ + 8x² step by step.

Step 1: Factor out the greatest common factor (GCF).  
Each term has a factor of 4x², so we factor that out:

4x⁴ - 12x³ + 8x² = 4x²(x² - 3x + 2)

Step 2: Factor the quadratic inside the parentheses.  
We have the quadratic x² - 3x + 2. Look for two numbers that multiply to 2 and add to -3.

These numbers are -1 and -2 because:  
  (-1) × (-2) = 2  
  (-1) + (-2) = -3

Thus, we can factor the quadratic as:

x² - 3x + 2 = (x - 1)(x - 2)

Step 3: Write the fully factored form.  
Substitute the factored quadratic back in:

4x⁴ - 12x³ + 8x² = 4x² (x - 1)(x - 2)

This is the final factored form of the expression.
The expression $$ 4x^{4} - 12x^{3} + 8x^{2} $$ can be factored as $$ 4x^{2}(x - 1)(x - 2) $$.

3. \( 4 x^{4}-12 x^{3}+8 x^{2} \)