How do you factor #3x^3-12x^2-45x#?

2 Answers
G_Ozdilek
Apr 24, 2017

You can write down #3x(x^2-4x-15)#

Explanation:

If you take a look at your equation, all numeric terms can be divided by 3. Also notice that x is the smallest term found in all terms. Now you can write down:

#3x(x^2-4x-15)#.

Mia
Apr 24, 2017

#=3x(x-(4+2sqrt19)/2)(x-(4-2sqrt19)/2)#

Explanation:

Factorization is determined either by taking common factor or
#" "#
computing #delta#
#" "#
#3x^3-12x^2-45x#
#" "#
#=3x(x^2-4x-15)#
#" "#
#delta=(-4)^2-4(1)(-15)#
#" "#
#delta=16+60#
#" "#
#delta=76#
#" "#
Since #delta>0# so #x^2-4x-15# admits two roots :
#" "#
The first root is:
#" "#
#x_1=(-(-4)+sqrt(76))/2#
#" "#
#x_1=(4+2sqrt19)/2#
#" "#
The second root is:
#" "#
#x_1=(-(-4)-sqrt(76))/2#
#" "#
#x_2=(4-2sqrt19)/2#
#" "#
Then :
#" "#
#x^2-4x-15=(x-(4+2sqrt19)/2)(x-(4-2sqrt19)/2)#
#" "#
Therefore:
#" "#
#3x^3-12x^2-45x#
#" "#
#=3x(x^2-4x-15)#
#" "#
#=3x(x-(4+2sqrt19)/2)(x-(4-2sqrt19)/2)#

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