Question

find the hcf of x^3-8x+3 and x^2+2x-3

Answer 1

Answer:

x + 3

Step-by-step explanation:

On this occasion, we can avoid things like long division and Euclid's Algorithm, because the quadratic is easy to factorize.  Specifically,

x² + 2x - 3 = ( x - 1 ) ( x + 3 ).

Are either of these factors also factors of the cubic?  By the Factor Theorem, x-1 is a factor if the cubic equates to 0 when we put x =  1, so lets check...

Putting x = 1 into the cubic gives 1 - 8 + 3 ≠ 0.  So x-1 is not a factor.

Now the same with x = -3, the cubic equates to -27 + 24 + 3 = 0.  So x+3 is a factor.