Question

Factorize: 9x4 - 6x3b + x262​

Answer 1

Answer:

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9x

4

−x

2

−12x−36

Above terms can be written as ,

9x

4

−(x

2

+12x+36)

We know that (a+b)

2

=a

2

+2ab+b

2

(3x

2

)

2

−(x

2

+∗2×6×x)+6

2

)

So (3x

2

)

2

−(x+6)

2

We know that a

2

−b

2

=(a+b)(a−b)

(3x

2

+x+6)(3x

2

−x−6)

Answer 2

Answer:

Answer:

The required factors are

3x^2+x+6\:\:and\:\:3x^2-x-63x

2

+x+6and3x

2

−x−6

Step-by-step explanation:

Formula used:

a^2-b^2=(a+b)(a-b)a

2

−b

2

=(a+b)(a−b)

Now,

\begin{gathered}9x^4-x^2-12x-36\\\\=9x^4-[x^2+12x+36]\\\\=(3x^2)^2-(x+6)^2\\\\=(3x^2+x+6)(3x^2-(x+6))\\\\=(3x^2+x+6)(3x^2-x-6)\end{gathered}

9x

4

−x

2

−12x−36

=9x

4

−[x

2

+12x+36]

=(3x

2

)

2

−(x+6)

2

=(3x

2

+x+6)(3x

2

−(x+6))

=(3x

2

+x+6)(3x

2

−x−6)