Question 822853
The goal is to factor. So we must find two numbers that multiply to -9 (last term) AND add to -8 (middle coefficient). These two numbers are +1 and -9, so we break up the middle term -8x^2 into +1x^2 - 9x^2 and we factor by grouping like so...


x^4-8x^2-9


x^4+x^2-9x^2-9


(x^4+x^2)+(-9x^2-9)


x^2(x^2+1)+(-9x^2-9)


x^2(x^2+1)-9(x^2+1)


(x^2-9)(x^2+1)


(x^2-3^2)(x^2+1)


(x-3)(x+3)(x^2+1) ... use the difference of squares rule here



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x^4-8x^2-9


completely factors to


(x-3)(x+3)(x^2+1)



So the final answer (that they want) is <font color="red">d) (x+3)</font>