Question

consider the following quadratic equation:
\\4x^2 = 9\\
step 1 of 2: using the standard form \\(ax^2 + bx + c = 0\\) of the given quadratic equation, factor the left hand side of the equation into two linear factors.

Explanation:

Rewrite in standard form

Using the Quadratic Functions knowledge point, we rearrange the given equation \(4x^2 = 9\) into the standard form \(ax^2 + bx + c = 0\) by subtracting \(9\) from both sides.

$$ 4x^2 - 9 = 0 $$

Identify the factoring pattern

Using the Difference of Squares knowledge point, we recognize that the left-hand side \(4x^2 - 9\) is a difference of two perfect squares.

$$ (2x)^2 - (3)^2 = 0 $$

Factor into linear factors

Using the Difference of Squares formula \(a^2 - b^2 = (a - b)(a + b)\), we factor the expression.

$$ (2x - 3)(2x + 3) = 0 $$

Answer:

Using the standard form \(ax^2 + bx + c = 0\) of the given quadratic equation, factor the left hand side of the equation into two linear factors.
<blank>\((2x - 3)(2x + 3)\)</blank> \(= 0\)