Algebra II factoring

posted by Lane

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).

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