#### A PHP Error was encountered

Severity: Warning

Message: count(): Parameter must be an array or an object that implements Countable

Filename: controllers/calculator.php

Line Number: 37

## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

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

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

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

The first two terms 6x2 - 8xy factor into 2x(3x - 4y)

The last two terms 15xy - 20y2 factor into 5y(3x - 4y)

So we get:

2x(3x -4y) + 5y(3x - 4y)

Step 4: The two new terms have a clearly visible common factor of (3x - 4y)

So we can now rewrite it like this:

2x(3x - 4y) + 5y(3x - 4y)

= (2x + 5y)(3x - 4y)