Factor: 22n2 + n - 5
22n^2 + n - 5
Use AC Method:
A*C = 22*(-5) = -110 = -10*11.
Select the pair of factors whose sum = B
=1: -10, and 11.
Form 2 factorable binomials:
22n^2 + (-10n+11n) - 5
(22n^2+11n) - (10n+5)
11n(2n+1) - 5(2n+1)
(2n+1)(11n-5)
To factor the given expression 22n^2 + n - 5, we can use the factoring method. This method involves finding two binomials that, when multiplied, give us the original expression.
Step 1: Multiply the coefficient of the leading term (22) by the constant term (-5). In this case, (22)(-5) = -110.
Step 2: Find two numbers whose product is -110 and whose sum is the coefficient of the middle term (1 in this case).
The pairs of factors for -110 are:
-1, 110
-2, 55
-5, 22
-10, 11
Since the sum of the factors should be 1, we can see that the pair -10, 11 satisfies this condition.
Step 3: Rewrite the middle term (1n) using these newly found numbers, -10 and 11. This can be done by splitting the original middle term and replacing it with two terms.
22n^2 - 10n + 11n - 5
Step 4: Group the terms in pairs and factor them separately.
(22n^2 - 10n) + (11n - 5)
Step 5: Factor out the greatest common factor from each pair.
2n(11n - 5) + 1(11n - 5)
Now we have factored out (11n - 5) as a common factor.
Step 6: Combine the two terms that have the common factor and write the final factored form.
(2n + 1)(11n - 5)
Therefore, the original expression 22n^2 + n - 5 can be factored into (2n + 1)(11n - 5).