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Quadratic Factoring Calculator

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Quadratic Factoring Calculator helps solving quadratic equation by finding the roots of the equation. Quadratic equation is in the form of $Ax^2 + Bx + C = 0$, where A, B are coefficients and C is constant and x is unknown. Plug in the values of a, b and c in this online quadratic factoring equation and find the factors of the equation.
 

Steps

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Step 1 : Check whether the equation is in the form of $Ax^2 + Bx + C = 0$ and note the coefficients of A, B and constant C.

Step 2 : By using the formula $D = b^2 - 4ac$, find the Discriminant (D).

Step 3 : Check if the discriminant is postive i.e., if D>0, then the roots are real. If not then the roots are imaginary.

Step 4 : Solutions of the equation are given in the form,
         $x$ = $\frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$

         $x_{1}$ = $\frac{(-b)  +  \sqrt{D}}{2a}$

         $x_{2}$= $\frac{(-b)  -  \sqrt{D}}{2a}$
         
$\therefore$ Factors will be shown as $(x - x_{1}) (x - x_{2})$.

Problems

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Below are the problems based on quadratic factoring.

Solved Examples

Question 1: Factor $x^2 - 3 = 2x$.
Solution:
Step 1 : Given equation $x^2 - 3 = 2x$
$x^2 - 2x - 3 = 0$

Coefficients are A = 1, B = -2 and C = -3.                   

Step 2 :Using the formula,
$D = b^2 - 4ac$
$D = (-2)^2 - 4(1)(-3)$
$D = 16$

Step 3 : Since D>0, the roots are real. 

Step 4 : Since D>0, the two solutions are given by,
$x$ = $\frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$

$x_{1}$ = $\frac{(-b) + \sqrt{D}}{2a}$ = $\frac{(-(-2)) + \sqrt{16}}{2(1)}$ = 3

$x_{2}$ = $\frac{(-b) - \sqrt{D}}{2a}$ = $\frac{(-(-2)) - \sqrt{16}}{2(1)}$ = -1

$\therefore$ Factors are $(x - 3)(x + 1)$. 


Question 2: Factor $x^2 - 12x + 27 = 0$.
Solution:
Step 1 : Given equation $x^2 - 12x + 27 = 0$

Coefficients are A = 1, B = -12 and C = 27.                   

Step 2 :  
Using the formula,
$D = b^2 - 4ac$
$D = (12)^2 - 4(1)(27)$
$D = 36$

Step 3 : Since D>0, the roots are real. 

Step 4 : Since D>0, the two solutions are given by,
$x$ = $\frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$

$x_{1}$ = $\frac{(-b) + \sqrt{D}}{2a}$ = $\frac{(-(-12)) + \sqrt{36}}{2(1)}$ = 9

$x_{2}$ = $\frac{(-b) - \sqrt{D}}{2a}$ = $\frac{(-(-12)) - \sqrt{36}}{2(1)}$ = 3

$\therefore$ Factors are $(x - 9)(x - 3)$.