11:45 76 ermathexpert.online Quiz Summary 17. Question Category: remainder Q17: Find the remainder when \( 3 x^{3}-2 x^{2}+4 x+5 \) is divided by \( 3 x+4 \). 1. -96 2. -23 3. -11 4. -1 Back Next

To find the remainder when dividing a polynomial by a linear binomial, you can use the Remainder Theorem. This theorem states that the remainder of the polynomial \( p(x) \) when divided by \( ax + b \) can be found by evaluating \( p\left(-\frac{b}{a}\right) \). In this case, you would evaluate \( 3x^3 - 2x^2 + 4x + 5 \) at \( x = -\frac{4}{3} \). Polynomials are everywhere in the real world! You’ll find polynomials in physics for motion equations, economics for profit calculations, and even in computer graphics for rendering images. Dividing polynomials is a nifty skill that can help you untangle complex problems and understand different real-world phenomena, making it incredibly useful for students and professionals alike!