Completely factor the polynomial, if possible. \begin{tabular}{ll}\( 9-16 x^{2} \) \\ Answer How to enter your answer (opens in new window) & 2 Points \\ Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is \\ used. \\ Keyboard Shortcuts \\ \hline \( \mathbf{x} \)\end{tabular}

To completely factor the polynomial \( 9 - 16x^2 \), we can recognize it as a difference of squares. This can be expressed as \( (3)^2 - (4x)^2 \), which allows us to use the identity \( a^2 - b^2 = (a - b)(a + b) \). Thus, we can factor it as: \[ (3 - 4x)(3 + 4x) \] Now the polynomial is factored completely. Factoring polynomials like this is crucial because it allows for easier manipulation and solving of equations. You can integrate, differentiate, or even graph the function more easily when it's in its simplest factored form. Plus, knowing how to identify special products, like the difference of squares, can streamline the problem-solving process and impress your math teacher! Many historical mathematicians have contributed to our understanding of factors and polynomials, but one standout is the Persian mathematician Al-Khwarizmi, whose work in the 9th century laid the groundwork for algebra. His approach to solving equations and factoring polynomials revolutionized mathematics and influenced cultures around the globe, making it essential for anyone studying this subject to appreciate the rich history behind these concepts!