At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
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]
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]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.