Final answer:
The trinomial 2x^2 - 22x + 48 is factored by finding two numbers that multiply to the product of the coefficient of x^2 and the constant term, and add to the coefficient of x. The factored form is (2x - 16)(x - 3).
Step-by-step explanation:
To factor the given trinomial 2x2 − 22x + 48, we need to find two numbers that multiply to 2 × 48 (the coefficient of x2 times the constant term) and add up to − 22 (the coefficient of x).
We can break down 48 into its prime factors to find suitable pairs that might work. After testing pairs, we find that − 6 and − 16 are the numbers we are looking for.
Now, we can express − 22x as − 6x − 16x and rewrite our trinomial:
2x2 − 6x − 16x + 48.
Then we can group terms to factor by grouping:
(2x2 − 6x) + (− 16x + 48).
We can factor out a 2x from the first group and a − 16 from the second, resulting in:
2x(x − 3) − 16(x − 3).
Finally, we factor out the common binomial factor (x − 3):
(2x − 16)(x − 3)
Therefore, the factored form of 2x2 − 22x + 48 is (2x − 16)(x − 3).