Respuesta :
When given an expression like this, the first step is to factor as much as you can and then look for common terms to divide out.
For K² + 9K + 20, we are looking to factor it. Our leading coefficient in front of K² is 1, so it's easier. We want a pair of numbers that multiply to 20 and add to 9. The pairs are: 1 and 20, 2 and 10, 4 and 5. Of those three, 4 and 5 add to 9, and we can check our work with FOIL.
(K + 4) (K + 5) = K² + 5K + 4K + 20 = K² + 9K + 20.
The process is similar for K² + 10K + 25: Look for a pair of numbers that multiply to the number and add to the middle term. For 25, there are only two pairs: 1 and 25, 5 and 5. 5 and 5 add to 10.
(K + 5)(K + 5) = K² + 10K + 25
For K² + 5K, there is a common K in each that can be divided out of each term. When you divide K, you are left with a K and a 5. Let's put it together.
K (K + 5) = K² + 5K
For K² -3K - 28, we need a pair that multiply to 28 but whose DIFFERENCE is 3 (because of the subtraction). Let's look for pairs: 1 and 28, 2 and 14, 4 and 7. 7 - 4 = 3, and we want the negative, so it's -7 and 4 that get to be the factors.
(K - 7) (K + 4) = K² - 7K + 4K = 28 = K² - 3K - 28
[Note: If you get +3k, then switch the signs.]
Now we factored all the things. Let's put it together. Divide out a common thing on the top and the bottom where you can.
K² + 9k + 20 / k² + 10k +25 • k² + 5k /k² - 3k -28
= (K + 4)(K + 5) / (K + 5)(K + 5) • (K)(K+5) / (K - 7)(K + 4) <---factor all the things
= (K + 4) / (K + 5) • (K)(K + 5) / (K - 7)(K + 4) <---divide out K + 5 on the left
= (K +4) / 1 • (K) / (K = 7) (K + 4) <---divide out K + 5 on bottom & top
= 1 / 1 • (K) / (K - 7) <---divide out K + 4 on bottom & top
= K / (K -7)
Thus the quotient is K / (K - 7)
Answer:
The answer above me is right
Step-by-step explanation:
