Solve Trinomial Problem: 2(2x^2+3x-14)

  • Thread starter Hollysmoke
  • Start date
  • Tags
    Factoring
In summary, the conversation is about factoring a trinomial problem (2x^2+3x-14) and the steps involved in solving it. The conversation includes a discussion on using the FOIL method and the possibility of factoring the problem with integer coefficients. The final answer is given as (2x+7)(x-2).
  • #1
Hollysmoke
185
0
I was working on this one trinomial problem-2(2x^2+3x-14) but I tried doing foil but I'm not sure what I am doing wrong. Could someone help me out? Thanks.
 
Physics news on Phys.org
  • #2
Are you solving for x?
 
  • #3
nope. Just trying to factor it.
 
  • #4
Well, you can't be "solving for x" since there is no equation! Since you titled this "Factoring Problem", guess you want to factor it further. That "2" in front has already been factored out and you can ignore it (until you are ready to write the answer).

The first step, then, is to factor 2x2+ 3x- 14. When you say you tried "FOIL", I was puzzled for a moment- that's really a mnemonic for multiplying, not factoring. But I suspect you really mean is:
The only way to factor 2 (into integer factors) is 2 and 1 so you must have (2x )(x ). There are two ways to factor 14: 1*14 and 2*7 and since you have -14, that gives -1*14, 1*(-14), -2*7, and 2*(-7)
That is- if it is possible to factor 2x2+ 3x- 14 with integer coefficients it must be one of:
(2x- 1)(x+ 14)
(2x+ 1)(x- 14)
(2x- 2)(x+ 7)
(2x+ 2)(x- 7)
(2x+14)(x- 1)
(2x-14)(x+ 1)
(2x- 7)(x+ 2)
(2x+ 7)(x- 2)
(2x+ 1)(x-14)
(2x- 1)(x+ 14)

Go ahead, multiply them and see if any work. You really only need to check the "cross terms"- the "O" and "I" of FOIL. Of course, there is no guarantee that this can be factored with integer coefficients!

Once you've figured out how to factor 2x2+ 3x- 14, don't forget to write that "2" factor.
 
  • #5
(2x+ 7)(x- 2)

Ahh thank you!
 
  • #6
u could always start with variables (ax+b)*(cx+d) multiply through
match them to each coefficent and solve =]
 

FAQ: Solve Trinomial Problem: 2(2x^2+3x-14)

What is a trinomial?

A trinomial is a polynomial expression with three terms.

How do you solve a trinomial problem?

To solve a trinomial problem, you can use the FOIL method, factoring, or the quadratic formula.

What does 2(2x^2+3x-14) mean?

This expression means to multiply each term inside the parentheses by the number 2. It can be rewritten as 4x^2+6x-28.

Can you factor 2(2x^2+3x-14)?

Yes, you can factor this trinomial by finding two numbers that multiply to the constant term (-28) and add to the coefficient of the middle term (3). In this case, the numbers are 7 and -4, so the trinomial can be factored as (2x+7)(x-4).

What are the solutions to 2(2x^2+3x-14)?

The solutions depend on the context of the problem. If the trinomial is set equal to 0, the solutions can be found by setting each factor equal to 0 and solving for x. In this case, the solutions are x=-7/2 and x=4. If the trinomial is not set equal to 0, the solutions will be different numbers.

Similar threads

Solve ##x^{\frac{-1}{2}}-2x^{\frac{1}{2}}+x^{\frac{2}{3}}=0##
Replies
24
Views
811
How do i factor cubic trinomials?
Replies
9
Views
34K
Factoring binomials with multiple variables p, x, and q
Replies
10
Views
2K
How Do You Solve Complex Absolute Value Inequalities?
Replies
4
Views
1K
Solve ##\dfrac{3x-6}{5-x}+\dfrac{11-2x}{10-4x}=3\dfrac{1}{2}##
Replies
3
Views
1K
Solving a nested logarithmic equation
Replies
2
Views
1K
Where Do the Graphs of |3x-2| and 1/x Intersect and Diverge?
Replies
4
Views
2K
Solving Plane Equation 3x + 2y -z = 4
Replies
8
Views
2K
Help! Factor Trinomial with X^3: Sample Problem Included
Replies
2
Views
3K
Solve for ##x## in the Given Problem
Replies
17
Views
1K

Hot Threads

Recent Insights

Back
Top