What two numbers have a product of -25 and a sum of 24?
1 answer:
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Answer: (3b + 5)(3b - 5)
Because both terms, 9b² and 25, are perfect squares, you can factor by taking the square roots of both terms.
The square root of 9b² is 3b (3b × 3b = 9b²).
The square root of 25 is 5 (5 × 5 = 25).
9b² - 25 has a negative, so the factored expression would be
(3b + 5)(3b - 5). The signs (+ and -) alternate in this case because the expression, 9b² - 25, has no middle term.
You can check your work by using FOIL. See the attachment below.
F irst
O utside
I nside
L ast
and
both have a common denominator, so you can combine them into a single fraction:
You cannot simplify this fraction further:
- - - - - - - - - - - - - - - - - - - -
Answer:
- - - - - - - - - - - - - - - - - - - - -