Final answer:
To factor the polynomial 3x² - 8x + 4, we can use the quadratic formula or factor by grouping. The factored form of the polynomial is (x - 2)(x - 2/3).
Step-by-step explanation:
To factor the polynomial 3x² - 8x + 4, we can use the quadratic formula or factor by grouping. Let's use the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 3, b = -8, and c = 4.
Substituting these values into the quadratic formula gives us:
x = (-(-8) ± √((-8)^2 - 4(3)(4))) / (2(3))
Simplifying further:
x = (8 ± √(64 - 48)) / 6
x = (8 ± √16) / 6
Now we can simplify the square root:
x = (8 ± 4) / 6
These two values give us the factors of the polynomial:
x = (8 + 4) / 6 = 2
x = (8 - 4) / 6 = 2/3
Therefore, the factored form of the polynomial 3x² - 8x + 4 is (x - 2)(x - 2/3).