Question

find hcf of 3x²+7x-6 and 2x²+7x+3​

Answer 1

Given:

The expression are:

$3x^2+7x-6$

$2x^2+7x+3$

To find:

The HCF of the given expression.

Solution:

We have,

$3x^2+7x-6$

$2x^2+7x+3$

The factor form of given expressions are:

$3x^2+7x-6=3x^2+9x-2x-6$

$3x^2+7x-6=3x(x+3)-2(x+3)$

$3x^2+7x-6=(x+3)(3x-2)$

Similarly,

$2x^2+7x+3=2x^2+6x+x+3$

$2x^2+7x+3=2x(x+3)+1(x+3)$

$2x^2+7x+3=(x+3)(2x+1)$

From the factor forms it is clear that the factor $(x+3)$ is common.

Therefore, the HCF of given expressions is $(x+3)$.