Question

D^3+6D^2+11D+6=0 how to find common factors?​

Answer 1

I have used X is place of d. First use guessing method (guess value of X) then if 0 is left, it's a factor. Divide p(X) by the factor and the split the quotient.

And there you go :-)

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Answer 2

$D^3\:+\:6D^2\:+\:11D\:+\:6 = \left(D+1\right)\left(D+2\right)\left(D+3\right)$

Solution:

Given equation is:

$D^3 + 6D^2 + 11D + 6 = 0$

Substitute D = -1

$(-1)^3 + 6(-1)^2 + 11(-1) + 6 \\\\-1 + 6 -11 + 6 \\\\12 - 12 = 0$

Thus,

(D + 1) is a factor

Now the given equation becomes,

$(D+1)(D^2+5D+6)$

Factorize

$D^2+5D+6 \\\\\mathrm{Break\:the\:expression\:into\:groups}\\\\\left(D^2+2D\right)+\left(3D+6\right)\\\\\mathrm{Factor\:out\:}D\mathrm{\:from\:}D^2+2D\mathrm{:\quad }\\\\\mathrm{Factor\:out\:}3\mathrm{\:from\:}3D+6\\\\D\left(D+2\right)+3\left(D+2\right)\\\\\mathrm{Factor\:out\:common\:term\:}D+2\\\\\left(D+2\right)\left(D+3\right)$

Thus the factors are:

$D^3\:+\:6D^2\:+\:11D\:+\:6 = \left(D+1\right)\left(D+2\right)\left(D+3\right)$

Thus the common factor are found

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