Factor the expression 12x+25x^2+40

 Exercise

$12x+25x^2+40$

 

Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($25$) to all terms

$25\left(x^2+\frac{12}{25}x+\frac{8}{5}\right)$

 

Add and subtract $\displaystyle\left(\frac{b}{2a}\right)^2$

$25\left(x^2+\frac{12}{25}x+\frac{8}{5}+\frac{36}{625}-\frac{36}{625}\right)$

 

Factor the perfect square trinomial $x^2+\frac{12}{25}x+\frac{36}{625}$

$25\left(\left(x+\frac{6}{25}\right)^2+\frac{8}{5}-\frac{36}{625}\right)$

 

Solve the product $25\left(\left(x+\frac{6}{25}\right)^2+\frac{8}{5}-\frac{36}{625}\right)$

$25\left(x+\frac{6}{25}\right)^2+25\cdot \left(\frac{8}{5}-\frac{36}{625}\right)$

$25\left(x+\frac{6}{25}\right)^2+25\cdot \left(\frac{8}{5}-\frac{36}{625}\right)$

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