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 x^{2}-5x+6 and x^{3}-27.

## HCF of X2-5x+6 and x3-27

### Factors of f(x) = x^{2}-5x+6

f(x) = x^{2}-5x+6

= x^{2}-3x-2x+6

= x(x-3)-2(x-3)

=(x-2)(x-3)

### Factors of q(x) x^{3}-27

q(x) = x^{3}-27

= x^{3}-3^{3}

= (x-3)(x^{2}+3x+9)

Note: Here we took the help of (a^{3}-b^{3}) = (a-b)(a^{2}+ab+b^{2})

Hence: the factors of x^{2}-5x+6 and x^{3}-27 are as follow:

Factors:

X2-5x+6 = (x-2)**(x-3)**

x3-27 = **(x-3)**(x^{2}+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) = x^{2}+5x+6 and q(x) + x^{3}+27

For finding out the highest common factors of these two Polynomial let’s do factors.

### Factors of quadratic polynomial x^{2}+5x+6

f(x) = x^{2}+5x+6

= x^{2}+5x+6

= x^{2}+2x+3x+6

= x(x+2)+3(x+2)

=(x+2)**(x+3)**

**Factors of polynomial x**^{3}+27

^{3}+27

q(x) = x^{3}+27

x^{3}+27

= **(x+3)**(x^{2}+9-3x)

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).

Factorization:

Factorization of 3×2-8x+5

Factorization of x2 -2x -8

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