Answer:
(a² +x +1)(a² -x -7)
Step-by-step explanation:
This expression can be factored by making use of the pattern for factoring the difference of squares. That pattern is ...
p² -q² = (p +q)(p -q)
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rearrange to difference of squares
We can split the term -7 into the sum +9-16 so that parts of the expression can be written as squares.
[tex]a^4 -6a^2-7-8x-x^2\\\\=(a^4-6a^2+9)-(16+8x+x^2)\qquad\text{use -7=9-16, group terms}\\\\=(a^2-3)^2-(4+x)^2\qquad\text{write as squares}[/tex]
factor using the pattern
[tex]=((a^2-3)+(4+x))\times((a^2-3)-(4+x))\qquad\text{factor using the pattern}\\\\=\boxed{(a^2+1+x)(a^2-7-x)}\qquad\text{simplify each factor}[/tex]
