Final answer:
The difference between the two polynomials 6g² +5g – 1 and 2g² +4g - 2 is 4g² + g + 1, which is obtained by changing the signs and combining like terms.
Step-by-step explanation:
To find the difference between two polynomials, you subtract the second polynomial from the first. In this case, the student is asked to subtract 2g² +4g - 2 from 6g² +5g – 1. The subtraction of polynomials is similar to the numerical example of 5-(+3) which equals 2, where you change the sign of each term in the polynomial being subtracted before adding.
Performing the subtraction:
Change the signs of the second polynomial: -2g² - 4g + 2.Add this to the first polynomial: (6g² + 5g - 1) + (-2g² - 4g + 2).Combine like terms: (6g² - 2g²) + (5g - 4g) + (-1 + 2).This simplifies to: 4g² + g + 1.
The difference is therefore 4g² + g + 1.