Factor the expression 16m^2-m+20

 Exercise

$16m^2-m+20$

 

Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($16$) to all terms

$16\left(m^2-\frac{1}{16}m+\frac{5}{4}\right)$

 

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

$16\left(m^2-\frac{1}{16}m+\frac{5}{4}+\frac{1}{1024}-\frac{1}{1024}\right)$

 

Factor the perfect square trinomial $m^2+-\frac{1}{16}m+\frac{1}{1024}$

$16\left(\left(m- \frac{1}{32}\right)^2+\frac{5}{4}-\frac{1}{1024}\right)$

 

Multiply the fraction and term in $- \frac{1}{32}$

$16\left(\left(m-\frac{1}{32}\right)^2+\frac{5}{4}-\frac{1}{1024}\right)$

 

Solve the product $16\left(\left(m-\frac{1}{32}\right)^2+\frac{5}{4}-\frac{1}{1024}\right)$

$16\left(m-\frac{1}{32}\right)^2+16\cdot \left(\frac{5}{4}-\frac{1}{1024}\right)$

$16\left(m-\frac{1}{32}\right)^2+16\cdot \left(\frac{5}{4}-\frac{1}{1024}\right)$

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