- #1
terryds
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Homework Statement
How to factor 2x^2 - (p-2)x - p ??
Homework Equations
Basic factoring
The Attempt at a Solution
I don't know how to do it.
The answer is 2(x-p/2)(x+2/2)..
Help me please..
Using quadratic roots formula?blue_leaf77 said:By finding its roots?
Yes.terryds said:Using quadratic roots formula?
It's very easy, you just need to pick that pen of yours and work it out on a paper.terryds said:It seems pretty complicated
As Blue Leaf posted, that will certainly work, but there is often an easier way. Assuming it has reasonable factors, you can factorise the first and last coefficients. This yields the only possibilities as (x ...)(2x...) and (... 1)(... p). There are two ways of merging those, and some number of options for the sign in between.terryds said:Using quadratic roots formula?
It seems pretty complicated
haruspex said:As Blue Leaf posted, that will certainly work, but there is often an easier way. Assuming it has reasonable factors, you can factorise the first and last coefficients. This yields the only possibilities as (x ...)(2x...) and (... 1)(... p). There are two ways of merging those, and some number of options for the sign in between.
I think there is actually a theorem about this.
You're welcome. For more info see https://en.wikipedia.org/wiki/Factorization#Finding_rational_rootsterryds said:Aha!
2x^2 + 2x - px - p= 0
2x (x+1) - p (x+1) =0
(2x-p)(x+1)=0
Thanks a lot! :D
Looks as if it's all solved very nicely.terryds said:Homework Statement
How to factor 2x^2 - (p-2)x - p ??
Homework Equations
Basic factoring
The Attempt at a Solution
I don't know how to do it.
The answer is 2(x-p/2)(x+2/2)..
Help me please..
Factoring a two variable function is the process of breaking down a polynomial expression with two variables into simpler expressions that can be multiplied together to get the original expression. It involves finding common factors between terms and grouping them together.
Factoring a two variable function is important because it helps simplify complex expressions and make them easier to work with. It also allows us to find the roots or solutions of the function, which are the values of the variables that make the expression equal to zero.
The steps for factoring a two variable function are:1. Identify any common factors between terms.2. Group the terms with common factors together.3. Factor out any GCF (Greatest Common Factor) from each group.4. Use the FOIL (First, Outer, Inner, Last) method to multiply the remaining terms in each group.5. Factor out any common factors between the two groups.6. Combine the terms to get the final factored expression.
No, not all two variable functions can be factored. Some functions may have complex or irrational roots, making it impossible to find a simplified factored form. In these cases, the function can be expressed using other methods such as the quadratic formula.
Factoring a two variable function is useful in real life because it can help solve problems involving multiple variables, such as in physics or engineering. It also allows us to find the minimum and maximum values of a function, which can be helpful in optimizing a process or finding the best solution to a problem.