Factor the expression 2x+1-5x^2

 Exercise

$\left(2x+1\right)-5x^2$

 

Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($-5$) to all terms

$-5\left(x^2-\frac{2}{5}x-\frac{1}{5}\right)$

 

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

$-5\left(x^2-\frac{2}{5}x-\frac{1}{5}+\frac{1}{25}-\frac{1}{25}\right)$

 

Factor the perfect square trinomial $x^2+-\frac{2}{5}x+\frac{1}{25}$

$-5\left(\left(x- \frac{1}{5}\right)^2-\frac{1}{5}-\frac{1}{25}\right)$

 

Multiply the fraction and term in $- \frac{1}{5}$

$-5\left(\left(x-\frac{1}{5}\right)^2-\frac{1}{5}-\frac{1}{25}\right)$

 

Solve the product $-5\left(\left(x-\frac{1}{5}\right)^2-\frac{1}{5}-\frac{1}{25}\right)$

$-5\left(x-\frac{1}{5}\right)^2-5\cdot \left(-\frac{1}{5}-\frac{1}{25}\right)$

$-5\left(x-\frac{1}{5}\right)^2-5\cdot \left(-\frac{1}{5}-\frac{1}{25}\right)$

 Try other ways to solve this exercise

Can't find a method? Tell us so we can add it.