Questions: Completely factor the polynomial, if possible 9x^2 - 16

Transcript text: Completely factor the polynomial. if possible \[ 9 x^{2}-16 \]

Solution

Solution Steps

Step 1: Identify the type of polynomial

The given polynomial is \( 9x^{2} - 16 \). This is a difference of squares, which can be factored using the formula: \[ a^{2} - b^{2} = (a + b)(a - b) \]

Step 2: Rewrite the polynomial as a difference of squares

Rewrite \( 9x^{2} - 16 \) in the form \( a^{2} - b^{2} \): \[ 9x^{2} = (3x)^{2}, \quad 16 = 4^{2} \] Thus, the polynomial becomes: \[ (3x)^{2} - 4^{2} \]

Step 3: Apply the difference of squares formula

Using the formula \( a^{2} - b^{2} = (a + b)(a - b) \), substitute \( a = 3x \) and \( b = 4 \): \[ (3x)^{2} - 4^{2} = (3x + 4)(3x - 4) \]