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Answer :
We start with the expression
[tex]$$35x^2 - 1.$$[/tex]
A common approach for factoring such expressions is to check if it can be written as a difference of two squares. Notice that
[tex]$$35x^2 = (\sqrt{35}\,x)^2 \quad \text{and} \quad 1 = 1^2.$$[/tex]
Thus, using the difference of squares formula
[tex]$$a^2 - b^2 = (a - b)(a + b),$$[/tex]
one could write
[tex]$$35x^2 - 1 = (\sqrt{35}\,x - 1)(\sqrt{35}\,x + 1).$$[/tex]
However, because [tex]$\sqrt{35}$[/tex] is irrational, this form is not expressed with rational coefficients. In many contexts (such as when factoring over the set of rational numbers), the expression
[tex]$$35x^2 - 1$$[/tex]
is considered already to be in its simplest factorized form.
Therefore, the final answer is:
[tex]$$35x^2 - 1.$$[/tex]
[tex]$$35x^2 - 1.$$[/tex]
A common approach for factoring such expressions is to check if it can be written as a difference of two squares. Notice that
[tex]$$35x^2 = (\sqrt{35}\,x)^2 \quad \text{and} \quad 1 = 1^2.$$[/tex]
Thus, using the difference of squares formula
[tex]$$a^2 - b^2 = (a - b)(a + b),$$[/tex]
one could write
[tex]$$35x^2 - 1 = (\sqrt{35}\,x - 1)(\sqrt{35}\,x + 1).$$[/tex]
However, because [tex]$\sqrt{35}$[/tex] is irrational, this form is not expressed with rational coefficients. In many contexts (such as when factoring over the set of rational numbers), the expression
[tex]$$35x^2 - 1$$[/tex]
is considered already to be in its simplest factorized form.
Therefore, the final answer is:
[tex]$$35x^2 - 1.$$[/tex]
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