Question

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

Answer 1

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.