Trinomials are nothing but the expressions that are in the form of a$x^{2}$+bx+c. By using step by step calculation we can find out the factors from the given equation.

If the coefficient of $x^{2}$ that is a = 1, we can find out all the factor pairs of 'c' otherwise multiply the 'a' value with 'c' and then find out the factor pairs. Then select one pair in a way that the sum of these number are equal to the 'b' value and factorize accordingly. The given problems will help you get a clear idea about trinomial factorization.

If the coefficient of $x^{2}$ that is a = 1, we can find out all the factor pairs of 'c' otherwise multiply the 'a' value with 'c' and then find out the factor pairs. Then select one pair in a way that the sum of these number are equal to the 'b' value and factorize accordingly. The given problems will help you get a clear idea about trinomial factorization.

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Let us discuss some problems regarding this topic.

### Solved Examples

**Question 1: **Factorizing $x^{2}$ + 3x + 2 ?

** Solution: **

Given equation is,

$x^{2}$ + 3x + 2

From the equation it is clear that a = 1, b = 3 and c = 2

Factor pairs of 2 is (1, 2), (-1, 2), (1, -2), (-1, -2)

Sum of the factor pair which gives 3 is (1,2)

So, $x^{2}$ + 3x + 2 = $x^{2}$ + x + 2x + 2

Factorizing the above equation we get,

$x^{2}$ + 3x + 2 = x(x + 1) + 2(x + 1)

$x^{2}$ + 3x + 2 = (x + 1)(x + 2)

**Question 2: **Factorizing the given equation, $x^{2}$ + 6x + 8 ?

** Solution: **

Given equation is,

$x^{2}$ + 6x + 8

From the equation it is clear that a = 1, b = 6 and c = 8

Factor pairs of 8 is (1,8), (-1,8), (1,-8), (-1,-8), (2,4), (-2,4), (2,-4), (-2,-4)

Sum of the factor pair which gives 6 is (2,4)

So, $x^{2}$ + 6x + 8 = $x^{2}$ + 2x + 4x + 8

Factorizing the above equation we get,

$x^{2}$ + 6x + 8 = x(x+2) + 4(x+2)

$x^{2}$ + 6x + 8 = (x+2)(x+4)

Given equation is,

$x^{2}$ + 3x + 2

From the equation it is clear that a = 1, b = 3 and c = 2

Factor pairs of 2 is (1, 2), (-1, 2), (1, -2), (-1, -2)

Sum of the factor pair which gives 3 is (1,2)

So, $x^{2}$ + 3x + 2 = $x^{2}$ + x + 2x + 2

Factorizing the above equation we get,

$x^{2}$ + 3x + 2 = x(x + 1) + 2(x + 1)

$x^{2}$ + 3x + 2 = (x + 1)(x + 2)

Given equation is,

$x^{2}$ + 6x + 8

From the equation it is clear that a = 1, b = 6 and c = 8

Factor pairs of 8 is (1,8), (-1,8), (1,-8), (-1,-8), (2,4), (-2,4), (2,-4), (-2,-4)

Sum of the factor pair which gives 6 is (2,4)

So, $x^{2}$ + 6x + 8 = $x^{2}$ + 2x + 4x + 8

Factorizing the above equation we get,

$x^{2}$ + 6x + 8 = x(x+2) + 4(x+2)

$x^{2}$ + 6x + 8 = (x+2)(x+4)