In factorization of quadratic trinomials there are two forms:

(i) First form: x(ii) Second form: ax

(i) Factorization of trinomial of the form x^2 + px + q:

Suppose we are given a quadratic trinomial xx

Solved examples on factorization of quadratic trinomials of the form x^2 + px + q:

The given expression is x

Find two numbers whose sum = -7 and product = 12

Clearly, such numbers are (-4) and (-3).

Therefore, x

= x(x - 4) -3 (x -
4)

= (x - 4)(x - 3).

The given expression is x

To factorize the given quadratic trinomial, we have to find two numbers a and b, such that a + b = 2 and ab = -15

Clearly, 5 + (-3) = 2 and 5 × (-3) = -15

Therefore such numbers are 5 and -3

Now, splitting the middle term 2x of the given quadratic trinomial x

x

= x(x +5) - 3(x + 5)

= (x + 5) (x - 3)

(ii) Factorization of trinomial of the form ax^2 + bx + c:

In order to factorize the expression axp + q = b and p × q = ac

Solved examples on factorization of quadratic trinomials of the form ax^2 + bx + c:

The given expression is 15x

Find two numbers whose sum = -26 and product = (15 × 8) = 120.

Clearly, such numbers are -20 and -6.

Therefore, 15x

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

= (3x - 4)(5x - 2).

Here, two numbers m and n are such that their sum m + n = -1 and their product m × n = 3 × (-4) i.e. m × n = - 12

Clearly, such numbers are -4 and 3

Now, splitting the middle term –q of the given quadratic trinomial 3q

3q

= q(3q – 4) + 1(3q – 4)

= (3q – 4)(q + 1)

**8th Grade Math Practice**

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