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

2 Answers
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).

Apr 24, 2017

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

Explanation:

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