1. What is each polynomial in standard form and what are the leading coefficient, the degree, and the number of terms of each? a. \( 2 x-3 x^{4}+6-5 x^{3} \) b. \( x^{5}+2 x^{6}-3 x^{4}-8 x+4 x^{3} \)

For the first polynomial \( -3 x^{4} + 2 x - 5 x^{3} + 6 \), the standard form is \( -3 x^{4} - 5 x^{3} + 2 x + 6 \). The leading coefficient is -3, the degree is 4, and there are 4 terms. For the second polynomial \( 2 x^{6} + x^{5} - 3 x^{4} + 4 x^{3} - 8 x \), the standard form is \( 2 x^{6} + x^{5} - 3 x^{4} + 4 x^{3} - 8 x \). The leading coefficient is 2, the degree is 6, and there are 5 terms. Understanding standard form helps to visualize the structure of polynomials, making it easier to identify key features like the degree and leading coefficient. This can be crucial in predictive modeling and graphing! When dealing with polynomials, it’s essential not to mix up the terms when ordering them. A common mistake is putting terms in an incorrect sequence or forgetting to combine like terms. Always start with the highest degree term to maintain the proper structure!