Question

P(x) = x^3 - 2x - 4 Factor P into linear and irreducible quadratic factors with real coefficients. 

          P(x) = x^3 - 2x - 4

Factor P into linear and irreducible quadratic factors with real coefficients.

Added by Erin A.

Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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P(x) = x^3 - 2x - 4 Factor P into linear and irreducible quadratic factors with real coefficients.
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Transcript

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00:01 So in this problem we need to factorize the polynomial given as linear and irreducible quadratic factor with the real coefficient and in second part we need to factor p completely into linear factors with complex coefficient so i'm doing a part so px is given as x cube minus 2x minus 4 so if we put x equals to 2 we get p 2 as 8 minus 4 minus 4 that is 0 so from here we can say that p 2 equals to 0 so x minus 2 is factor of x q minus 4 in order to find other factor we need to divide by x minus 2 and polynomial is x q minus 2x minus 4 so first we multiply with x x x square we get x q minus 2x square sign will change so this will cancel out so we are left with 2x square minus 2x minus 4 so we multiply with 2x so we will multiply with 2x so we will multiply with 2x so we get 2x square minus 4x so in this case this would be minus this would be plus so this will be cancelled out so we are left with 2x minus 4.
01:51 So we will take 2 plus 2.
01:55 So this would be 2x minus 4.
01:57 Sign will change minus and plus.
01:59 So we are left with no reminder.
02:02 So x cube minus 2x minus 4 can be written as 1 factor x minus 2 and x square plus 2x plus 2...
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