One of the factors of $$9x^2 - 4z^2 - 24xy + 16y^2 + 20y - 15x + 10$$ is

Solution

Grouping, $$9x^2-24xy+16y^2=(3x-4y)^2$$, and writing $$u=3x-4y$$, the expression becomes $$u^2-4z^2-5u+10z$$, which factors as $$(u-2z)(u+2z-5)$$. Substituting back gives $$(3x-4y-2z)(3x-4y+2z-5)$$, so $$3x-4y-2z$$ is a factor.

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