1Cademy - Factoring $$18x^2 - 3xy

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Factoring Trinomials of the Form $ax^2 + bx + c$ Using Trial and Error

Example

Factoring $18x^2 - 3xy - 10y^2$

To factor the two-variable trinomial $18x^2 - 3xy - 10y^2$ using trial and error, evaluate combinations of factors from the first and last terms. The factor pairs for the first term $18x^2$ include $x \cdot 18x$ , $2x \cdot 9x$ , and $3x \cdot 6x$ . Because the last term $-10y^2$ is negative, its factors must have opposite signs, such as $2y$ and $-5y$ . Test different binomial combinations to find the arrangement where the sum of the inner and outer products equals the middle term, $-3xy$ . Selecting the binomials $(3x + 2y)$ and $(6x - 5y)$ results in an outer product of $-15xy$ and an inner product of $12xy$ . Adding these together gives $-15xy + 12xy = -3xy$ , which matches the middle term. Thus, the completely factored form is $(3x + 2y)(6x - 5y)$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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