Answer :
Final answer:
The correct factors of the quadratic expression 2[tex]x^2[/tex] - 9x - 35 are D. (2x - 5) and (x + 7).
Explanation:
To factor the quadratic expression 2² - 9x - 35, we look for two binomials that multiply to the expression. We can do this by breaking down the middle term (-9x) into two terms that multiply to the product of the leading coefficient (2) and the constant term (-35), which is -70. We need to find two numbers that add up to -9 and multiply to -70. These numbers are -10 and +7.
So, we rewrite the middle term (-9x) as -10x + 7x:
2x² - 10x + 7x - 35
Now we can group the terms and factor by grouping:
(2x² - 10x) + (7x - 35)
Factor out the greatest common factor from each group:
2x(x - 5) + 7(x - 5)
Now, notice that both groups have the common factor (x - 5). We can factor this out:
(x - 5)(2x + 7)
So, the quadratic expression factors into (x - 5) and (2x + 7). In the given answer choices, option D is the correct factorization: 2x - 5, and x + 7. This correctly identifies the factors of the quadratic expression.(Option D)
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