Ontario Mathematics Proficiency Practice Test

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Question: 1 / 400

How do you factor the expression x² - 9?

(x + 9)(x - 9)

(x - 3)(x - 3)

(x + 3)(x - 3)

To factor the expression x² - 9, we recognize that it is a difference of squares. The formula for factoring a difference of squares is a² - b² = (a + b)(a - b). In this case, we can identify a as x and b as 3, since 9 is the square of 3.

Applying the difference of squares formula, we have:

x² - 9 = x² - 3² = (x + 3)(x - 3).

This correctly breaks down the expression into two binomial factors, which are the sum and difference of the square root of 9, indicating that the roots of the equation x² - 9 = 0 are x = 3 and x = -3. This confirms that (x + 3)(x - 3) is indeed the correct factorization of the expression.

The other options represented various other combinations of factors that do not result in the original expression when multiplied, confirming that they do not follow the difference of squares principle.

Ontario Mathematics Proficiency Practice Test

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