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Math Help - Factoring Polynomials

  1. #1
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    Question Factoring Polynomials

    Hello, Im new to factoring polynomials:

    6st + 15t -10s -25

    (6st + 15t) + (-10s -25) <-- Grouped polynomials

    Common factors of both groups:
    (6st + 15t) --> 3t
    (-10s -25) --> -5

    Now factor out the common factor from each group:
    = 3t(2s + 5) -5(2s + 5)

    The common factor is the binomials but what are the steps to factoring this out? I lost here.

    tyvm
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by 4lgebra View Post
    Hello, Im new to factoring polynomials:

    6st + 15t -10s -25

    (6st + 15t) + (-10s -25) <-- Grouped polynomials

    Common factors of both groups:
    (6st + 15t) --> 3t
    (-10s -25) --> -5

    Now factor out the common factor from each group:
    = 3t(2s + 5) -5(2s + 5)

    The common factor is the binomials but what are the steps to factoring this out? I lost here.

    tyvm
    Hi 4lgebra,

    (2s + 5) is common to both terms, so (2s + 5)(3t - 5) and you're done.

    Maybe, look at it this way.

    3t(2s + 5) -5(2s + 5)

    Let x = (2s + 5)

    3tx - 5x

    Factor out the x

    x(3t - 5)

    Replace x with (2s + 5) and we have (2s + 5)(3t - 5).
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  3. #3
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    Factoring Polynomials:

    Masters,

    Thank you for clearing that up for me, I appreciate you taking the time to respond.

    In closing... When factoring, if I have "opposites" like a - b , how is -(a - b) its opposite? My text says these values are opposites, but it assumes I already know why they are opposites.

    ty bye
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by 4lgebra View Post
    Masters,

    Thank you for clearing that up for me, I appreciate you taking the time to respond.

    In closing... When factoring, if I have "opposites" like a - b , how is -(a - b) its opposite? My text says these values are opposites, but it assumes I already know why they are opposites.

    ty bye
    Hi 4lgebra,

    The opposite of a value is defined as being the negative of the value. In other words, the opposite of 5 is -5. The opposite of -4 is 4, and so on. If a variable represents a value, then the opposite of x would be -x. The opposite of (a - b) would be -(a - b).

    If you think of a value as being a certain distance from zero on the number line, it's opposite would be the same distance from zero going in the opposite direction.
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  5. #5
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    Factoring Polynomials

    masters,

    That is exactly the information I needed. Thank you for all your help and God bless.

    4~
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