I need help. i am having trouble factoring trinomials into binomials.
an example problem is 4n^2-5n-6
can someone show me step by step how to factor these kind of problems easily?
Take the coefficient of your quadratic term in this case 4 and multiply it by your constant term in this case -6. You get -24. Then you want to figure out two numbers which when multiplied together give you -24 and when added together give you the value of the coefficient of your linear term in this case -5.
So, the two numbers are -8 and 3.
Take those two numbers and rewrite your problem changing you linear term in this case -5n using -8 and 3.
Changed problem is: 4n^2-8n+3n-6
Now factor by grouping. The first two terms can be factored into 4n(n-2) and the last two terms can be factored into 3(n-2). Notice you have the same factor in parentheses.
So, the original problem (4n^2-5n-6)can be factored into (4n+3)(n-2).
To factor trinomials into binomials, you can follow these steps:
Step 1: Identify the coefficients.
In your example problem 4n^2 - 5n - 6, the coefficient of the quadratic term is 4, the coefficient of the linear term is -5, and the constant term is -6.
Step 2: Multiply the quadratic coefficient by the constant term.
Multiply 4 and -6, resulting in -24.
Step 3: Find two numbers that multiply to give you the result from Step 2 and add up to the coefficient of the linear term.
In this case, we need to find two numbers that multiply to -24 and add up to -5. The two numbers are -8 and 3 because (-8) * (3) = -24 and (-8) + (3) = -5.
Step 4: Rewrite the trinomial using the numbers from Step 3.
Rewrite the original trinomial by replacing the linear term -5n with -8n + 3n:
4n^2 - 8n + 3n - 6
Step 5: Factor by grouping.
Now, we can group the terms and factor them separately. Group the first two terms and the last two terms:
(4n^2 - 8n) + (3n - 6)
Step 6: Factor out common factors from each group.
Factor out the common factor from the first group, which is 4n:
4n(n - 2)
Factor out the common factor from the second group, which is 3:
3(n - 2)
Step 7: Simplify and combine the factors.
The factors of the trinomial can be written as:
(4n + 3)(n - 2)
So, the factored form of the original trinomial 4n^2 - 5n - 6 is (4n + 3)(n - 2).