Question

Write each polynomial in standard form. Then, give the leading coefficient 4g³+8g-4g³+ 2g²

Answer 1

The polynomial 4g³+8g-4g³+2g² simplifies to 2g²+8g when written in standard form after canceling the like terms. The leading coefficient of the polynomial is 2.

Step-by-step explanation:

To write the polynomial 4g³+8g-4g³+2g² in standard form, we combine like terms and arrange it in descending order of the exponents of the variables.

First, combine the like terms, which are the terms with g³:

• 4g³ and -4g³ cancel each other out, so they result in 0.

Next, we simply list the remaining terms in descending order of their exponents:

• 2g² (since it has the highest exponent now)
• 8g (since it has the next highest exponent)

The polynomial in standard form is 2g² + 8g. The leading coefficient is the coefficient of the term with the highest power, which is 2 in this case.