Dear viewers here is the Highest Common Factor HCF of X2-5x+6 and x3-27. With step by step solution.
First of all, we will do factors of these both x2-5x+6 and x3-27.
HCF of X2-5x+6 and x3-27
Factors of f(x) = x2-5x+6
f(x) = x2-5x+6
Factors of q(x) x3-27
q(x) = x3-27
Note: Here we took the help of (a3-b3) = (a-b)(a2+ab+b2)
Hence: the factors of x2-5x+6 and x3-27 are as follow:
X2-5x+6 = (x-2)(x-3)
x3-27 = (x-3)(x2+3x+9)
Here the HCF or Highest Common Factor is (x-3).
H.C.F. of X2-5x+6 and x3-27 is x-3.
Another Example HCF of X2+5x+6 and x3+27
Our elements are f(x) = x2+5x+6 and q(x) + x3+27
For finding out the highest common factors of these two Polynomial let’s do factors.
Factors of quadratic polynomial x2+5x+6
f(x) = x2+5x+6
Factors of polynomial x3+27
q(x) = x3+27
From both Polynomial we can see that (x+3) is the common factor.
Highest Common Factors or H.C.F. of X2+5x+6 and x3+27 is (x+3).