**Box method factoring :**

Here we are going to see how to factor a quadratic equation using box method.

A equation which is in the form ax^{2} + bx + c known as quadratic equation.

Let us look into some example problems to understand the above concept.

**Example 1 :**

Factor 3x^{2} + 19x + 6

**Solution : **

**Step 1 :**

Draw a box, split it into four parts.

Write the first and last term in the first and last box respectively.

**Step 2 :**

Multiply the coefficient of x^{2} by the last term and find the factors of this number. The simplified values of those factors must be equal to the middle term.

**Step 3 :**

Factor horizontally and vertically

Factor x from the 1 |
Factor 6 from the 2 |

Factor 3x from the 1 |
Factor 1 from the 2 |

3x^{2} + 19x + 6 = (x + 6) (3x + 1)

Hence the factors of the given quadratic equation are (x + 6) and (3x + 1)

**Example 2 :**

Factor 5y^{2} - 29y + 20

**Solution : **

**Step 1 :**

Draw a box, split it into four parts.

Write the first and last term in the first and last box respectively.

**Step 2 :**

Multiply the coefficient of y^{2} by the last term and find the factors of this number. The simplified values of those factors must be equal to the middle term.

Since the middle term is negative, both factors will have negative sign.

**Step 3 :**

Factor horizontally and vertically

5y^{2} - 29y + 20 = (5y - 4) (y - 5)

Hence the factors of the given quadratic equation are (5y - 4) and (y - 5)

**Example 3 :**

Factor 2x^{2} + 17x - 30

**Solution : **

**Step 1 :**

Draw a box, split it into four parts.

Write the first and last term in the first and last box respectively.

**Step 2 :**

Multiply the coefficient of x^{2} by the last term and find the factors of this number. The simplified values of those factors must be equal to the middle term.

Since the last term is negative, the factors will be in the combination of positive and negative.

**Step 3 :**

Factor horizontally and vertically

2x^{2} + 17x - 30 = (x + 10) (2x - 3)

Hence the factors of the given quadratic equation are (x + 10) and (2x - 3)

**Example 4 :**

Factor 18x^{2} - x - 4

**Solution : **

**Step 1 :**

Draw a box, split it into four parts.

Write the first and last term in the first and last box respectively.

**Step 2 :**

Multiply the coefficient of x^{2} by the last term and find the factors of this number. The simplified values of those factors must be equal to the middle term.

Since the middle and last term are negative, the factors will be in the combination of positive and negative.

**Step 3 :**

Factor horizontally and vertically

18x^{2} - x - 4 = (2x - 1) (9x + 4)

Hence the factors of the given quadratic equation are (2x - 1) and (9x + 4)

After having gone through the stuff given above, we hope that the students would have understood "Box method factoring".

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