Factor the trinomial.
5c^c-70c+200
= 5(c^2 - 14c + 40) , I assume that was c^2
- 5(c-10)(c-4)
do you mean
5 c^2 - 70 c + 200 ????
5 [ c^2 - 14 c + 40 ]
5 (c-4)(c-10)
To factor the trinomial 5c^2 - 70c + 200, we need to rewrite it in the form (ac^2 + bc + c).
First, we can look for a common factor among the three terms. In this case, all terms have a common factor of 5, so we can factor it out:
5(c^2 - 14c + 40)
Next, we need to find two numbers that multiply to 40 (the coefficient of c^2 term times the constant term) and add up to -14 (the coefficient of the c term). These two numbers will be the factors we need to factor the trinomial.
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40.
Now, we need to find two numbers from the list above that add up to -14. After trying different combinations, we can see that -10 and -4 add up to -14.
Therefore, we can rewrite -14c as -10c - 4c:
5(c^2 - 10c - 4c + 40)
Next, we group the terms so we can factor by grouping:
(c^2 - 10c) - (4c - 40)
Now, we can factor out a common factor from each group:
c(c - 10) - 4(c - 10)
Notice that we have a common factor of (c - 10) in both terms. We can now factor it out:
(c - 10)(c - 4)
So, the factored form of the trinomial 5c^2 - 70c + 200 is (c - 10)(c - 4).