Find the HCF: x²-9, x³-27 and x²+x-12. | HCF and LCM | SciPiPupil

Find the HCF: $x^2-9, \;x^3-27\;and;\;x^2+x-12$.

This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the description below. If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts.

Solution:

Given,

$1^{st} expression = x^2-9$

= $x^2-3^2$

= $(x+3)(x-3)$

$2^{nd} expression = x^3-27$

= $x^3-3^3$

= $(x-3)(x^2-3x+9)$

$3^{rd} expression = x^2+x-12$

= $x^2+(4-3)x-12$

= $x^2+4x-3x-12$

= $(x+4)(x-3)$

Therefore, the HCF = $(4x^2+2x+1)$

Explanation to the above answer.

Step 1: Write the first expression given in the question.

Step 2: We write the expression in the form of (a²-b²).

Step 3:  We write the factor formula of (a²-b²) as (a+b)(a-b).

Step 4: Write the second expression given in the question.

Step 5: Write the second expression in the form of (a³-b³).

Step 6: Now, write the factor formula of (a³-b³) = (a-b)(a²+ab+b²).

Step 7: Write the third expression given in the question.

Step 8: We need to factorize the third expression given in the question. For this, we use mid-term factorization method.

Step 9: Write the expression after performing the operation in parenthesis.

Step 10: Now, write the factor of the expression. From step 9, we get: x(x+4) -3(x+4) = (x+4)(x-3).

Step 11: Write the H.C.F. (Highest Common Factor) of the given expressions by analysing the factors you generated in each expressions. Here, (x-3) are the common factors.

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Question: Find the HCF: x²-9, x³-27 and x²+x-12. | HCF and LCM | SciPiPupil

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