Use the grouping method to factorize common terms: $2x^{2}+3xy-10x-15y\rightarrow x(2x+3y)-5(2x+3y)\rightarrow (x-5\)\cdot \left ( 2x+3y \right )$ $\displaystyle 2x^{2}+3xy-10x-15y\rightarrow x(2x+3y)-5(2x+3y)\rightarrow (x-5$\cdot \left ( 2x+3y \right )\)

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Example Question #12 : Express A Polynomial As A Product Of Linear Factors

Factorize the following polynomial expression completely to its linear factors: $f(x)=10x^{2}-4x+15xy-6y$ $\displaystyle f(x)=10x^{2}-4x+15xy-6y$

Possible Answers:

$(2x+3y)\cdot (5x-2)$ $\displaystyle (2x+3y)\cdot (5x-2)$

$(2x+3y\cdot (5x+2)$ $\displaystyle (2x+3y\cdot (5x+2)$

$(2x-3y\cdot (5x+2)$ $\displaystyle (2x-3y\cdot (5x+2)$

$(2x+3)\cdot (5x-2)$ $\displaystyle (2x+3)\cdot (5x-2)$

Correct answer:

$(2x+3y)\cdot (5x-2)$ $\displaystyle (2x+3y)\cdot (5x-2)$

Explanation:

Use the grouping method to factorize common terms: $10x^{2}-4x+15xy-6y\rightarrow 2x(5x-2)\rightarrow (2x+3y)\cdot (5x-2)$ $\displaystyle 10x^{2}-4x+15xy-6y\rightarrow 2x(5x-2)\rightarrow (2x+3y)\cdot (5x-2)$

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Precalculus : Express a Polynomial as a Product of Linear Factors

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