Factor the expression -3x^2+7x+17

 Exercise

-3x^2+7x+17

 

Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$ . Take common factor $a$ ( $-3$ ) to all terms

-3\left(x^2-\frac{7}{3}x-\frac{17}{3}\right)

 

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

-3\left(x^2-\frac{7}{3}x-\frac{17}{3}+\frac{49}{36}-\frac{49}{36}\right)

 

Factor the perfect square trinomial $x^2+-\frac{7}{3}x+\frac{49}{36}$

-3\left(\left(x- \frac{7}{6}\right)^2-\frac{17}{3}-\frac{49}{36}\right)

 

Multiply the fraction and term in $- \frac{7}{6}$

-3\left(\left(x-\frac{7}{6}\right)^2-\frac{17}{3}-\frac{49}{36}\right)

 

Solve the product $-3\left(\left(x-\frac{7}{6}\right)^2-\frac{17}{3}-\frac{49}{36}\right)$

-3\left(x-\frac{7}{6}\right)^2-3\cdot \left(-\frac{17}{3}-\frac{49}{36}\right)

-3\left(x-\frac{7}{6}\right)^2-3\cdot \left(-\frac{17}{3}-\frac{49}{36}\right)

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