Factorize: 9x4 - 6x3b + x262
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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)
Answered by
4
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)
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