224k views
2 votes
For the function h(x)=8(x−9)(x−5)^2, determine the leading term.

A) 8x^4
B) 8x^3
C) 8x^2
D) 8x

1 Answer

1 vote

Final answer:

The leading term of the function h(x)=8(x−9)(x−5)^2 is obtained by expanding the terms and identifying the term with the highest power of x, leading to the term 8x^3, which corresponds to option B.

Step-by-step explanation:

To determine the leading term of the function h(x)=8(x−9)(x−5)2, you need to expand the function and identify the term with the highest power of x. Multiplying the terms out, we get:

h(x)=8(x−9)(x−5)(x−5)

First, let's focus on the square term:

(x−5)2 = x2 - 10x + 25

Now, multiplying this result by the remaining (x−9), we have:

(x2 - 10x + 25)(x−9)

We are only interested in the leading term, which comes from multiplying the highest powers of x together:

x2 × x = x3

And finally, multiplying by the coefficient 8, we get:

8 × x3 = 8x3

Therefore, the leading term of the function is 8x3, which corresponds to option B) 8x3.

User Valor
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.