**Factoring trinomials box method :**

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)

Let us look into the next problem on "Factoring trinomials box method".

**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)

- Factoring expressions
- Factoring polynomials
- Factoring linear expressions
- Factoring quadratics when a is not equal to 1
- Solving polynomials by factoring quadratic equations

After having gone through the stuff given above, we hope that the students would have understood "Factoring trinomials box method".

If you want to know more about the stuff "Factoring trinomials box method" Please click here

Apart from the stuff "Factoring trinomials box method" given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**