Q. 15.0( 1 Vote )

# Let's find the G.C.D. of the algebraic expressions x(x2– 9), x2 – x – 12.

Let us understand what a G.C.D, Greatest Common Divisor is.

The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

To find G.C.D of x(x2 – 9) and x2 – x – 12, let us write down factors of each term.

Factorization of x(x2 – 9) = x(x – 3)(x + 3)

[, by algebraic identity, a2 – b2 = (a – b)(a + b)]

For factorization of x2 – x – 12,

x2 – x – 12 = x2 – 4x + 3x – 12 [, Sum of -4 and 3 is -1 and multiplication is -12]

x2 – x – 12 = x(x – 4) + 3(x – 4) [, common from the first two terms is x and last two terms is 3]

x2 – x – 12 = (x – 4)(x + 3) [, common from the two terms is (x – 4)]

So, factorization of x2 – x – 12 = (x – 4)(x + 3)

Find the factors that these two lists share in common.

Factors of x(x2 – 9) = x, (x – 3), (x + 3)

Factors of x2 – x – 12 = (x – 4), (x + 3)

Common factor that is found in these two terms is (x + 3).

Thus, the gcd of x(x2 – 9) and x2 – x – 12 is (x + 3).

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Multiplication of Algebraic Expression40 mins  Division of Algebraic Expressions36 mins  Algebraic Expressions and Identities43 mins  Division of Algebraic Expressions37 mins  Algebric Expressions and Identities45 mins  How to Use Algebraic Identities40 mins  Genius Quiz | Algebraic Expressions and Identities30 mins  Operations on Algebraic Expressions51 mins  NCERT | Practice Qs on Addition and Subtraction of Algebraic Expressions42 mins  Master Algebraic Identities43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 