Question

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

Answer 1

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)`.

Answer 2

`=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)`