Final Answer:
The factored form of the polynomial 4x² - 9x + 5 by grouping is:
(4x - 5)(x - 1).
Step-by-step explanation:
To factor the given quadratic polynomial 4x² - 9x + 5 by grouping, we look for pairs of terms whose coefficients have a common factor. In this case, we observe that the coefficient of the quadratic term (4) can be factored into 2 * 2, and the constant term (5) cannot be factored further. Now, we break down the middle term (-9x) into two terms whose coefficients multiply to give the product of the quadratic term's coefficient and the constant term. The terms -4x and -5x satisfy this condition, as -4x * (-5x) = 20x², which is the product of 2 * 2 and 5.
So, we rewrite the middle term -9x as -4x - 5x. Now, we group the terms:
4x² - 4x - 5x + 5
Next, we factor out the common factor from the first two terms and the last two terms:
4x(x - 1) - 5(x - 1)
Now, we can factor out the common factor of (x - 1):
(4x - 5)(x - 1)
Thus, the factored form of 4x² - 9x + 5 by grouping is (4x - 5)(x - 1).