Question

How to factor the polynomials (2x+3)(3x-5)

Answer 1

Assignment: $\bold{Simplify \ Equation: \ \left(2x+3\right)\left(3x-5\right)}$

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Answer: $\boxed{\bold{6x^2-x-15}}$

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Explanation: $\downarrow\downarrow\downarrow$

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[ Step One ] Apply Foil Method

Note: $\bold{Foil \ Method: \ \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd}$

$\bold{a=2x,\:b=3,\:c=3x,\:d=-5}$

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$\bold{2x\cdot \:3x+2x\left(-5\right)+3\cdot \:3x+3\left(-5\right)}$

[ Step Two ] Apply Addition / Subtraction Rules

Note: $\bold{Addition \ / \ Subtraction \ Rules: \ +\left(-a\right)=-a}$

$\bold{2\cdot \:3xx-2\cdot \:5x+3\cdot \:3x-3\cdot \:5}$

[ Step Three ] Simplify $\bold{2\cdot \:3xx-2\cdot \:5x+3\cdot \:3x-3\cdot \:5}$

$\bold{6x^2-x-15}$

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$\bold{\rightarrow Mordancy \leftarrow}$