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Two algebraic expressions [tex]$x^2 - 5x + 6[tex]$[/tex] and [tex]$[/tex]x^2 - 9$[/tex] are given.

Find the HCF of the given expressions.

Sagot :

GinnyAnswer
To find the Highest Common Factor (HCF) of the given algebraic expressions \( x^2 - 5x + 6 \) and \( x^2 - 9 \), follow these steps:

1. Factorize Each Expression:

- For \( x^2 - 5x + 6 \), we look for factors of 6 that add up to -5. Those factors are -2 and -3, so we can write:
[tex]\[ x^2 - 5x + 6 = (x - 2)(x - 3) \][/tex]

- For \( x^2 - 9 \), recognize that this is a difference of squares. We can write:
[tex]\[ x^2 - 9 = (x - 3)(x + 3) \][/tex]

2. Identify Common Factors:

- Both factorizations contain the factor \( x - 3 \):
[tex]\[ x^2 - 5x + 6 = (x - 2)(x - 3) \][/tex]
[tex]\[ x^2 - 9 = (x - 3)(x + 3) \][/tex]

3. Determine the HCF:

The common factor between the two factorizations is \( x - 3 \).

Therefore, the HCF of the expressions \( x^2 - 5x + 6 \) and \( x^2 - 9 \) is:
[tex]\[ x - 3 \][/tex]
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