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[Solved] Polynomial factoring linear polynomials

 
Polynomials
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June 15, 2021 11:39 am
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If the polynomial  6x^2-5xy-4y^2-11x+22y+m  can be factored into the product of two linear polynomials, find the value of  m  and factor the polynomial.

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June 15, 2021 11:39 am
Topic starter
Staff 
(@armor)
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Let   6x^2-5xy-4y^2-11x+22y+m=(2x+y+k)(3x-4y+l) 

=6x^2-5xy-4y^2+(3k+2l)x+(l-4k)y+kl,  then equaling the coefficients:

\small 3k+2l=-11, l-43k+2l=-11, l-4k=22, kl=m,  which result in    k=-5, l=2, m=-10.

Hence    6x^2-5xy-4y^2-11x+22y+m=6x^2-5xy-4y^2-11x+22y-10

=(2x+y-5)(3x-4y+2)

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