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Polynomial factorization: FAQ

Frequently asked questions about polynomial factorization

What is factoring?

Factoring is the process of breaking down a polynomial into smaller pieces (or "factors") that, when multiplied together, will give you the original polynomial.

Why do we factor polynomials?

Factoring is a useful technique for solving polynomial equations. By breaking a polynomial down into smaller factors, we can often simplify the equation and find the solutions more easily.

What is a monomial?

A monomial is a polynomial with just one term. For example, 2x, 3y2, and 5 are all monomials.

What is the greatest common factor?

The greatest common factor (GCF) of two or more terms is the largest factor that all the terms have in common. For example, the GCF of 6x2 and 9x is 3x.

How do we take common factors out of a polynomial?

To take common factors out of a polynomial, we divide each term by the GCF. For example, to factor 6x2+9x, we divide both terms by the GCF, 3x, to get 3x(2x+3).

What are polynomial identities?

Polynomial identities are equations that are true for all values of the variable. For example, the difference of squares identity, a2b2=(a+b)(ab), is true for any values of a and b.

Where are these topics used in the real world?

There are many applications for factoring polynomials. For example, engineers may use these techniques in signal processing or control theory, while scientists might use them in modeling physical phenomena.

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  • blobby green style avatar for user 26huangd
    does this finite geo series formula always work? or is there a specific restriction for the variables?
    (4 votes)
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    • blobby blue style avatar for user joshua
      Geometric series always work except where common ratio = r = 1, since the denominator will be zero. But when r = 1, you can easily claim that all terms in the series are equal.

      Other than that, the geometric series will always work.
      (27 votes)
  • blobby green style avatar for user zaaraz.fashion
    Can anyone explain geometric series in simple lang
    (2 votes)
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    • stelly blue style avatar for user bingai
      A geometric series is a sequence of numbers that follow a pattern where each term is obtained by multiplying the previous term by a fixed number. For example, the sequence 1, 2, 4, 8, 16, … is a geometric series because each term is twice the previous term. The fixed number that we multiply by is called the common ratio.

      The formula for finding the sum of an infinite geometric series is a / (1 - r), where a is the first term and r is the common ratio. If |r| < 1, then the sum of the series is finite and can be calculated using this formula. If |r| >= 1, then the series diverges and does not have a finite sum.

      For example, consider the geometric series 1 + 2 + 4 + 8 + .... Here, a = 1 and r = 2. Since |r| >= 1, this series diverges and does not have a finite sum.
      (15 votes)
  • duskpin tree style avatar for user Nicole
    why is it when r is a percentage, it can be written as 1.the percentage or 0.the percentage? for example 10% was converted to 1.1 and not 0.1 but 90% was 0.9 and not 1.9
    (3 votes)
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  • blobby green style avatar for user mackenzievs
    No lie, if I wanna be a nurse what would this math have to do with anything?
    (3 votes)
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  • blobby green style avatar for user eshanpradhan0115
    for the earlier section we used the formula where "a" was included numerator section but now im using it like this?
    a(1-r^n/1-r)?
    (4 votes)
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  • leafers tree style avatar for user Spartan117
    my brain is fried. Is there any way to make finite series easier, maybe some tips or tricks? I especially need help with finding the first term using the formula
    (3 votes)
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    • starky sapling style avatar for user Shaurya Yadav
      I don't use any "tricks" but I just ignore the 'a' in the equation until get the final fraction which I multiply to the other side of the equation to isolate the 'a'. Ex. 25/27 x a = 57. You multiply the 25/27 by its reciprocal which is 27/25 to cancel it and you do the same to the other side of the equation to isolate the a on its own.
      (1 vote)
  • blobby green style avatar for user Noma Woodall
    how do you find the minimum of a degree on a graph?
    (3 votes)
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  • duskpin ultimate style avatar for user DNAstrid
    I had troubles with understanding this section, it was completely out of the blue and the answers seemed to be random and did not match what the problem was. Could someone clarify the process for me?
    (2 votes)
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  • male robot hal style avatar for user Viqnix
    this is very very confusing help me please
    (1 vote)
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  • blobby green style avatar for user Greg One
    In deriving the geo series formula, why are the 2 lines added together? What is the reason? Tnx!
    (0 votes)
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    • blobby purple style avatar for user Lotup
      They are equivalent expressions, and since they are equivalent, when you add one to the other, you are adding the same thing to both sides.

      e.g.

      a = 12
      now lets square both sides to make another equation
      a^2 = 12^2
      now add both equations
      a + a^2 = 12 + 12^2

      it's still equivalent. Seems pointless here but as you saw from the video and you will see in the future, this allows us to manipulate equations in ways we couldn't do otherwise (e.g. in the geometric series, it allows us to add/subtract an infinitely repeating series to get a formula to solve for the variables in the series).
      (3 votes)