Question

The GCD of the polynomials is (x + 3) and their LCM is (x-7x+6). If one of the polynomials is (x² + 2x - 3), then the other is​

Answer 1

Answer:

We know

product of two numbers = GCD x LCM

$lcm \: = {x}^{2} - 7x + 6 = (x - 1)(x - 6) \\ gcd \: = x + 3 \\ a \: = {x}^{2} + 2x - 3 = (x + 3)(x - 1) \\ so \\ a \times b = gcd \times lcm \\ b = gcd \times lcm \div a \\ b = \frac{(x - 1)(x - 6)(x + 3)}{(x + 3)(x - 1)} \\ so \: b \: = x - 6$