In this section, we are going to see some examples on factoring quadratic expressions.

Before look at the examples, if you would like to know how to factor quadratic expressions,

Example 1 :

Factor :

x2 + 13x + 30

Solution :

In the given quadratic expression, the coefficient of x2 is 1.

Decompose the constant term +30 into two factors such that the product of the two factors is equal to +30 and the addition of two factors is equal to the coefficient of x, that is +13.

Then, the two factors of +30 are

+3 and +10

Factor the given quadratic expression using +3 and +10.

x2 + 13x +30  =  (x + 3)(x + 10)

Therefore, the factors of the given quadratic expression are

(x + 3) and (x + 10)

Example 2 :

Factor :

x2 + 22x + 21

Solution :

In the given quadratic expression, the coefficient of x2 is 1.

Decompose the constant term +21 into two factors such that the product of the two factors is equal to +21 and the addition of two factors is equal to the coefficient of x, that is 22.

Then, the two factors of -21 are

+1 and +21

Factor the given quadratic expression using +1 and +21.

x2 + 22x + 21  =  (x + 1)(x + 21)

Therefore, the factors of the given quadratic expression are

(x + 1) and (x + 21)

Example 3 :

Factor :

x2 + 3x – 28

Solution :

In the given quadratic expression, the coefficient of x2 is 1.

Decompose the constant term -28 into two factors such that the product of the two factors is equal to -28 and the addition of two factors is equal to the coefficient of x, that is +3.

Then, the two factors of -28 are

-4 and +7

Factor the given quadratic expression using -4 and +7.

x2 + 3x – 28  =  (x - 4)(x + 7)

Therefore, the factors of the given quadratic expression are

(x - 4) and (x + 7)

Example 4 :

Factor :

x2 – x – 30

Solution :

In the given quadratic expression, the coefficient of x2 is 1.

Decompose the constant term -30 into two factors such that the product of the two factors is equal to -30 and the addition of two factors is equal to the coefficient of x, that is -1.

Then, the two factors of -30 are

-6 and +5

Factor the given quadratic expression using -6 and +5.

x2 – x – 30  =  (x - 6)(x + 5)

Therefore, the factors of the given quadratic expression are

(x - 6) and (x + 5) After having gone through the stuff given above, we hope that the students would have understood how to factor quadratic equations.

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