apple_pi
Factor: x^42x^3+x^2+8x5
Try it manually...how is it done?



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ParthKohli
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Use the rational roots test?

apple_pi
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try it

ParthKohli
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Okay. The possible rational roots are:
5
5
1
1

ParthKohli
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Checking all of them. Gimme a sec.

hartnn
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forget 1,1

ParthKohli
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Yup, not 1 and 1.

ParthKohli
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not 5.

hartnn
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no rational roots

apple_pi
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yeah, but it can still be factorised

Algebraic!
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into two quadratics... what's the point here?

apple_pi
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Well...you're factoring it
I guess you could get the roots
But how do you get to the quadratics?

ParthKohli
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Yeah, we can.

hartnn
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i may suggest a way,
(x^2+ax+b)(x^2+cx+d) = x^42x^3+x^2+8x5
and compare the coefficients,
4 unknowns

hartnn
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like bd=5

ParthKohli
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Like for example, we have \(\sqrt2{}\) as a root, then a factor would be \(\rm x^2  2\).

AbhimanyuPudi
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Well, @hartnn 's way is very good to get the quadratics