Question

Write -2x^3(4x^3 + 5x^6) in standard form, classify the degree, and find the end behavior.

Answer 1

Just did one like that, your turn.

Answer 2

Just did it and got this one right

-10x^9 -8x^6; 9th degree; up to down
Good luck with the rest!

Answer 3

[AI-generated answer — Step-by-Step Bot]

To simplify the expression -2x^3(4x^3 + 5x^6), you need to distribute the -2x^3 to each term inside the parentheses:

-2x^3 * 4x^3 + (-2x^3) * 5x^6

Now, simplify each term separately:

-8x^6 + (-10x^9)

Combining like terms, the expression becomes:

-8x^6 - 10x^9

To write it in standard form, arrange the terms in descending order of exponents:

-10x^9 - 8x^6

The degree of the expression is determined by the highest exponent, which is 9. So, the degree is 9.

The end behavior refers to how the graph of the expression behaves as x approaches positive infinity or negative infinity.

As x becomes larger and larger (approaching infinity), the -10x^9 term dominates the expression. Since the coefficient is negative (-10), the end behavior is negative infinity.

Similarly, as x becomes smaller and smaller (approaching negative infinity), the -10x^9 term still dominates, and the negative coefficient (-10) causes the end behavior to be negative infinity.

Therefore, the end behavior of the expression -10x^9 - 8x^6 is negative infinity for both positive and negative infinity.

Answer 4

[AI-generated answer — Explain Bot]

To simplify the expression -2x^3(4x^3 + 5x^6) and write it in standard form, you need to multiply the terms inside the parentheses by the term outside the parentheses:

-2x^3 * 4x^3 = -8x^6 (multiply the coefficients, -2 and 4, and add the exponents x^3 and x^3, which gives you x^6)
-2x^3 * 5x^6 = -10x^9 (multiply the coefficients, -2 and 5, and add the exponents x^3 and x^6, which gives you x^9)

Combine the results:

-8x^6 - 10x^9

This is the expression in standard form.

To classify the degree, you need to identify the highest power of x in the expression. In this case, the highest power of x is x^9. Therefore, the degree of the expression is 9.

To find the end behavior, you need to analyze how the expression behaves as x approaches positive infinity and negative infinity.

As x approaches positive infinity, the term -8x^6 dominates the expression because x^9 grows much faster as x increases. Therefore, as x approaches positive infinity, the end behavior is that the expression becomes very negative.

As x approaches negative infinity, the term -10x^9 dominates the expression because negative values of x raised to an odd power (-10 x^9) will also be negative. Therefore, as x approaches negative infinity, the end behavior is that the expression becomes very negative.

In summary, the end behavior of the expression -2x^3(4x^3 + 5x^6) is that it becomes very negative as x approaches both positive and negative infinity.