Question

Factorise 12x^2 + 27x + 6 in the form of (ax + 3)(cx + 2) by using the method of splitting the middle term and find the values of a and c.

Answer 1

Answer:

Refer the attachment:)

Answer 2

Given:

12x² + 27x + 6

Required form of factors = (ax + 3) (cx + 2)

To Find:

Factors of the given expression and values of a and c.

Solution:

Splitting the middle term of the expression,

12x² + (24 + 3)x + 6

12x² + 24x + 3x + 6

now,

12x (x + 2) + 3 (x + 2)

which is,

(12x + 3) (x + 2)

Comparing the factors with the required forms,

(ax + 3) = (12x + 3) and,

(cx + 2) = (x + 2)

by this, a = 12 and c = 1

Hence, the factors of the given expression in the required form are (12x + 3) and (x + 2). The values of a and c are 12 and 1.