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Help me with factoring please

Please help me with this Brilliant polynomial factoring by grouping. I have no idea how to do this so i answer 1 to get to view the solution. The solution, however, is use less to me. Can someone please explain and teach me how to solve this problem step by step please? Thank you so much.

I understand how it can be rewritten in the first line(although i have no idea what should be rewritten) but i don't know how to transform it to the second line(How to change it to a product of two trinomials) Thank you for your help

Note by Peter Bishop
4 years ago

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Put \( x^2 - 5x = y \)

Then you'll get

\( \rightarrow y ^2 - 18y -144 \)

\( \rightarrow y ^ 2 - 24y + 6y -144 \)

\( \rightarrow y(y - 24) + 6(y - 24) \)

\( \rightarrow (y+6)(y-24) \)

Putting \( y = x^2 - 5x \)

\( \rightarrow (x^2 - 5x + 6)(x^2 - 5x - 24) \)

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Great job, Siddhartha. Recognizing a change of variables can often help you to easily deal with algebraic manipulation. In this case, factoring a quartic equation is as simple as a quadratic equation.

I thought that giving the factorization in terms of \( (x^2 - 5x) \) made the substitution obvious. I'd add in more details to this solution. Thanks for your feedback, Peter.

Calvin Lin Staff - 4 years ago

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