Which is the completely factored form of 12x4 + 39x3 + 9x2?

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caylus caylus · Answer 1 · 2016-07-01T14:00:52+02:00

Hello,

12x^4+39x^3+9x²=x²(12x²+39x+9)=x²(12x²+36x+3x+9)=x²(4x(3x+9)+(3x+9))
=x²(3x+9)(4x+1)
=3x²(x+3)(4x+1)

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RenatoMattice RenatoMattice · Answer 2 · 2019-01-03T10:45:13+01:00

Answer: The completely factored form will be

[tex]3x^2(4x+1)(x+3)[/tex]

Step-by-step explanation:

Since we have given that

[tex]12x^4 + 39x^3 + 9x^2[/tex]

We need to find the factored form,

So, here we go:

1) Taking out the common factor i.e. 3x² :

[tex]12x^4 + 39x^3 + 9x^2\\\\3x^2(4x^2+13x+3)[/tex]

2) We get a quadratic equation , we will split the middle term:

[tex](4x^2+13x+3)\\\\4x^2+12x+x+3=0\\\\4x(x+3)+1(x+3)=0\\\\(4x+1)(x+3)=0[/tex]

3) Now, combine the all of the factors:

[tex]3x^2(4x+1)(x+3)[/tex]

Hence, the completely factored form will be

[tex]3x^2(4x+1)(x+3)[/tex]