1. \( 8 x^{2}-4 x+12 \) 2. \( 3 x^{2}-2 x^{4}+2 x-1 \) 3. \( -2 x^{6}-3 x^{4}+2 x^{2}-x+2 \) 4 \( -2 x^{3}+4 x^{2}-5 x-1 \) 4) How many terms are there in thise

Let’s break it down! The number of terms in a polynomial is simply the count of distinct parts that are summed together. 1. The polynomial \( 8x^{2}-4x+12 \) has 3 terms: \( 8x^{2} \), \( -4x \), and \( 12 \). 2. The polynomial \( 3x^{2}-2x^{4}+2x-1 \) also has 4 terms: \( -2x^{4} \), \( 3x^{2} \), \( 2x \), and \( -1 \). 3. The polynomial \( -2x^{6}-3x^{4}+2x^{2}-x+2 \) contains 5 terms: \( -2x^{6} \), \( -3x^{4} \), \( 2x^{2} \), \( -x \), and \( 2 \). 4. Finally, the polynomial \( -2x^{3}+4x^{2}-5x-1 \) has 4 terms: \( -2x^{3} \), \( 4x^{2} \), \( -5x \), and \( -1 \). So, in total, the number of terms across the four polynomials are 3, 4, 5, and 4 respectively! Understanding the structure of polynomials not only helps in counting, but also in recognizing how each term interacts with others in algebraic operations. Fun fact: Polynomials are essentially the building blocks of many complex mathematical concepts, including calculus and even statistics! They help in modeling everything from populations to profits!