Can this trinomial be factored?

  • Thread starter Byrgg
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In summary, the conversation was about a student's math homework where the teacher put DNF for one answer, but the student was able to factor the trinomial correctly. They discuss the possibility of DNF meaning "did not finish" or if the teacher wanted the 3 factored out. However, it is determined that the student's factorization is correct and the teacher may have made a mistake. The conversation ends with the student thanking the others for their help.
  • #1
Byrgg
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My math teacher put up the answers from yesterday's homework, and she put DNF for one of the answers, which I'm assuming means does not factor. But I'm pretty sure I found a way to factor it, here's the trinomial:

3v^2 - 11v + 10

I factored it and came up with the following:

(3v - 5)(v - 2)

Was my teacher just wrong, or did I make a mistake?
 
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  • #2
well when its multiplied out it equals the same thing. maybe DNF means 'did not finish'...maybe she wanted the 3 factored out for some reason. ie: 3(v-5/3)(v-2)
 
  • #3
Nope, your factorisation looks good to me, I would agree with you that your polynomial does indeed factor as you have shown.

Edit: I need to type faster!
 
  • #4
For the trinomial above, your answer is right.

Edit: And I need to type faster than Hoot! :biggrin:
 
  • #5
that makes me the fastest!
 
  • #6
Ok, thanks for the help.

dmoravec said:
maybe DNF means 'did not finish'...maybe she wanted the 3 factored out for some reason. ie: 3(v-5/3)(v-2)

No, it wasn't my work that she put DNF on, she had an overhead screen, with all of the answers on it, and for that question, she simply put DNF.
 
  • #7
well i'd have to say she is mistaken
 

1. Can every trinomial be factored?

No, not every trinomial can be factored. Some trinomials, known as prime trinomials, cannot be factored any further.

2. How do I know if a trinomial can be factored?

There are a few different methods to determine if a trinomial can be factored. One method is to use the discriminant, which is the part of the quadratic formula that is inside the square root. If the discriminant is a perfect square, then the trinomial can be factored. Another method is to try to factor the trinomial using the AC method or by using the reverse FOIL method.

3. What is the AC method for factoring trinomials?

The AC method, also known as the grouping method, is a way to factor trinomials that have a coefficient greater than 1 in front of the squared term. It involves finding two numbers that multiply to equal the product of the first and last terms in the trinomial, and then using those numbers to rewrite the middle term. This allows for the trinomial to be factored by grouping the first two terms and the last two terms together.

4. Can a trinomial be factored if the coefficient of the squared term is negative?

Yes, a trinomial can still be factored if the coefficient of the squared term is negative. The factoring process is the same as if the coefficient was positive, but the resulting factors will have opposite signs.

5. Are there any special cases when factoring trinomials?

Yes, there are a few special cases when factoring trinomials. One special case is when the trinomial is a perfect square, which means it can be factored into two identical binomials. Another special case is when the trinomial is a difference of squares, which can be factored into the sum and difference of the square roots of the first and last terms.

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