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Quadratic Factoring Calculator

Quadratic Factoring Calculator

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Quadratic factoring calculator is used to find the factors for polynomial equation. Quadratic equation is in the

form of ax^2+bx+c=0, Here ‘a’ is the coefficient of x ^2, ‘b’ is the coefficient of x and c is the constant number.

To factor a polynomial equation, break the expression as multiples of two expressions.




Example 1: Find the factor for 6x^2+x-2.


Solution steps:

Step 1: Product of terms =6*-2 =-12

Sum of terms = x

So we want two numbers that add up to get x, and multiply together to make -12.

In fact -3 and 4 do that (-3x + 4x = x, and -3 × 4 = -12)

Step 2: Rewrite the middle with these numbers:

Rewrite x with -3x and 4x:

6x2 - 3x + 4x - 2

Step 3: Factor out the first two and last two terms individually:

The first two terms 6x2 - 3x factor into 3x(2x - 1) and

The last two terms 4x - 2 factor into 2(2x - 1)

So we get 3x (2x - 1) + 2(2x - 1)

Step 4:  So we can now rewrite it like this:

3x(2x - 1) + 2(2x - 1) = (3x + 2)(2x - 1)




Example 2: find the factors for 6x^2 + 7xy – 20y^2.


Solution steps:

Step 1:  product of terms = 6 × -20 = -120

Sum of terms =7xy

so we want two numbers that add up to 7, and multiply together to make -120.

In fact -8 and 15 do that: -8xy + 15xy = 7xy, and -8 × 15 = -120

Step 2: Rewrite the middle with these numbers:

Rewrite 7xy with -8xy and 15xy:

6x2 - 8xy + 15xy - 20y2 

 

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