Factor the expression 8x^2-30x+7

 Exercise

$8x^2-30x+7$

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Factor the trinomial $8x^2-30x+7$ of the form $ax^2+bx+c$, first, make the product of $8$ and $7$

$\left(8\right)\left(7\right)=56$

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Now, find two numbers that multiplied give us $56$ and add up to $-30$

$\begin{matrix}\left(-2\right)\left(-28\right)=56\\ \left(-2\right)+\left(-28\right)=-30\end{matrix}$

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Rewrite the original expression

$8x^2-28x-2x+7$

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Factor $8x^2-28x-2x+7$ by the greatest common divisor $4$

$4\left(2x^2-7x\right)-2x+7$

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Factoring by $x$

$4x\left(2x-7\right)-2x+7$

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Factoring by $2x-7$

$\left(2x-7\right)\left(4x-1\right)$

$\left(2x-7\right)\left(4x-1\right)$

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