Factor the trinomial.
v2−4v−60
To factor the trinomial v^2 - 4v - 60, we need to find two numbers that multiply to give -60 and add up to -4.
The factors of -60 are: -1 and 60, -2 and 30, -3 and 20, -4 and 15, -5 and 12, -6 and 10.
Among these factors, the pair that adds up to -4 is -10 and 6.
So, we can rewrite the trinomial as:
v^2 - 10v + 6v - 60
Now we can group the terms:
(v^2 - 10v) + (6v - 60)
Factor out the greatest common factor from each group:
v(v - 10) + 6(v - 10)
Now we can factor the common binomial:
(v + 6)(v - 10)
Therefore, the trinomial v^2 - 4v - 60 can be factored as (v + 6)(v - 10).
To factor the trinomial v^2 - 4v - 60, we need to find two numbers that multiply to -60 and add up to -4.
The factors of -60 are:
-1 and 60
-2 and 30
-3 and 20
-4 and 15
-5 and 12
-6 and 10
Out of these pairs of numbers, the pair that adds up to -4 is -10 and 6.
So, we can rewrite the trinomial as follows:
v^2 - 10v + 6v - 60
Next, we group the terms:
(v^2 - 10v) + (6v - 60)
Now, we factor out the greatest common factor from each group.
v(v - 10) + 6(v - 10)
Finally, we can factor out the common binomial factor (v - 10) from both terms.
(v - 10)(v + 6)
Therefore, the factored form of the trinomial v^2 - 4v - 60 is (v - 10)(v + 6).
To factor the trinomial v^2 - 4v - 60, we can use the factoring by grouping method. Here's how you can do it:
Step 1: Multiply the coefficient of the leading term (v^2) by the constant term (-60). In this case, it is -60.
Step 2: Look for two numbers that multiply to -60 and add up to the coefficient of the middle term (-4). The two numbers that meet this condition are -10 and 6. (-10 * 6 = -60 and -10 + 6 = -4)
Step 3: Rewrite the middle term (-4v) using the two numbers found in step 2. Split -4v as -10v + 6v. This gives us the trinomial v^2 - 10v + 6v - 60.
Step 4: Group the terms and factor by common factors. In our case, we have v^2 - 10v + 6v - 60. We can group the first two terms and the last two terms: (v^2 - 10v) + (6v - 60).
Step 5: Factor out the greatest common factor from each group. In the first group, factor out 'v' to get v(v - 10). In the second group, factor out '6' to get 6(v - 10).
Step 6: Notice that both groups have a common factor (v - 10). Factor out the common factor to obtain the final factored form: (v - 10)(v + 6).
Therefore, the factored form of the trinomial v^2 - 4v - 60 is (v - 10)(v + 6).