Get detailed and reliable answers to your questions with IDNLearn.com. Discover prompt and accurate answers from our experts, ensuring you get the information you need quickly.
Sagot :
To factor the polynomial [tex]\(x^2 - 62\)[/tex], you need to follow these steps:
1. Recognize the polynomial structure:
The given polynomial is [tex]\(x^2 - 62\)[/tex], which is a difference of squares.
2. Recall the formula for difference of squares:
The difference of squares formula is [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex]. Here, [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are any expressions.
3. Identify the expressions for [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
In the polynomial [tex]\(x^2 - 62\)[/tex], we can see it as:
[tex]\[ a^2 = x^2 \quad \text{and} \quad b^2 = 62 \][/tex]
Therefore,
[tex]\[ a = x \quad \text{and} \quad b = \sqrt{62} \][/tex]
4. Apply the difference of squares formula:
Substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the formula:
[tex]\[ x^2 - 62 = (x - \sqrt{62})(x + \sqrt{62}) \][/tex]
So, the factors of the polynomial [tex]\(x^2 - 62\)[/tex] are:
[tex]\[ (x - \sqrt{62})(x + \sqrt{62}) \][/tex]
1. Recognize the polynomial structure:
The given polynomial is [tex]\(x^2 - 62\)[/tex], which is a difference of squares.
2. Recall the formula for difference of squares:
The difference of squares formula is [tex]\(a^2 - b^2 = (a - b)(a + b)\)[/tex]. Here, [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are any expressions.
3. Identify the expressions for [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
In the polynomial [tex]\(x^2 - 62\)[/tex], we can see it as:
[tex]\[ a^2 = x^2 \quad \text{and} \quad b^2 = 62 \][/tex]
Therefore,
[tex]\[ a = x \quad \text{and} \quad b = \sqrt{62} \][/tex]
4. Apply the difference of squares formula:
Substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the formula:
[tex]\[ x^2 - 62 = (x - \sqrt{62})(x + \sqrt{62}) \][/tex]
So, the factors of the polynomial [tex]\(x^2 - 62\)[/tex] are:
[tex]\[ (x - \sqrt{62})(x + \sqrt{62}) \][/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.