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Math Help - How do I find the linear factor?

  1. #1
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    How do I find the linear factor?

    Hello, I need help with the following. could someone please help?

    Find the linear factor of the form x-a, when a is a constant, of the cubic polynomial

    f(x) = x^3+2x^2+2x +4 and hence factorise f(x)
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Begin by grouping the terms like this

    (x^3+2x^2)+(2x+4)

    now factor

    x^2(x+2)+2(x+2)

    You can see that (x+2) is a factor of both terms, and now it can be fatored out like so

    (x+2)(x^2+2)

    Does that help? There are alot of ways to approach expressions of degree>2. Your goal is to know them all and to be able to know when is the right time to use the appropriate method.

    Oh, I almost forgot. You need the linear factor in the form (x-a), but x+2=x-(-2), therefore a=-2

    Got it?
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  3. #3
    Senior Member TheAbstractionist's Avatar
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    Quote Originally Posted by gva0324 View Post
    Hello, I need help with the following. could someone please help?

    Find the linear factor of the form x-a, when a is a constant, of the cubic polynomial

    f(x) = x^3+2x^2+2x +4 and hence factorise f(x)
    Hi gva0324.

    The constant a is where f(a)=0. Good candidates to try for a are the divisors of the constant term, in this case \pm1,\,\pm2,\,\pm4. You can also look at the polynomial and make a few eliminations. In this case, all the coefficients are positive, so you must try a negative number. Also all but one of the coefficients are even, so \pm1 are no good. Therefore, you should try f(-2) and f(-4) and see which is 0.
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