Question

Factorize 3x^3-12x^2-x+4​

Answer 1

Answer:

Factorization is determined either by taking common factor or

computing δ

3x3−12x2−45x

=3x(x2−4x−15)

δ=(−4)2−4(1)(−15)

δ=16+60

δ=76

Since δ>0 so x2−4x−15 admits two roots :

The first root is:

x1=−(−4)+√762

x1=4+2√192

The second root is:

x1=−(−4)−√762

x2=4−2√192

Then :

x2−4x−15=(x−4+2√192)(x−4−2√192)

Therefore:

3x3−12x2−45x

=3x(x2−4x−15)

=3x(x−4+2√192)(x−4−2√192)

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