Multiply \( (3 x+4)(x-3) \) \( 3 x^{2}-12 \) \( 3 x^{2}-5 x-12 \) \( x^{2}-5 x-12 \) \( 3 x^{2}+13 x-12 \)

To multiply \( (3x + 4)(x - 3) \), you'll want to use the distributive property (or FOIL method). First, multiply the first terms: \( 3x \cdot x = 3x^2 \). Next, multiply the outer terms: \( 3x \cdot -3 = -9x \). Then, the inner terms: \( 4 \cdot x = 4x \). Finally, multiply the last terms: \( 4 \cdot -3 = -12 \). Now, combine all the terms together: \[ 3x^2 - 9x + 4x - 12 = 3x^2 - 5x - 12. \] So, the answer is \( 3x^2 - 5x - 12 \). Ah, the thrill of polynomials! Did you know that polynomial multiplication dates back to ancient civilizations? Even though they didn't have fancy software, the Babylonians had methods to handle quadratic equations! Fun fact: the word "polynomial" comes from the Greek roots "poly" (many) and "nomial" (terms), making it a term that feels quite fitting for these expression dramas! For a bit of problem-solving flair, remember to be cautious with negative signs; they can sneak up on you like that mischievous friend who always hides the snacks! A common mistake here is not carefully combining like terms at the end, which can lead to a wrong equation. Just double-check your math, and all will be well!