Factor the expression 5-4t-t^2

 Exercise

$5-4t-t^2$

 

Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($-1$) to all terms

$-\left(t^2+4t-5\right)$

 

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

$-\left(t^2+4t-5+4-4\right)$

 

Factor the perfect square trinomial $t^2+4t+4$

$-\left(\left(t+2\right)^2-5-4\right)$

 

Subtract the values $-5$ and $-4$

$-\left(\left(t+2\right)^2-9\right)$

 

Solve the product $-\left(\left(t+2\right)^2-9\right)$

$-\left(t+2\right)^2+9$

$-\left(t+2\right)^2+9$

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