Leading term of -20(x - 2)^15 (4-x)^11

Question

asked Oct 17, 2021 33.1k views

2 Answers

Mitchelllc · Answer 1 · 2021-10-18T01:08:57+0000

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Work Shown:

The leading term for (x-2)^15 is x^15

The leading term for (4-x)^11 is -x^11

Multiply the outer value -20 with each of those leading terms to get

-20*x^15*(-x^11)

20x^(15+11)

20x^26

which is the leading term of -20(x - 2)^15 (4-x)^11

GgPeti · Answer 2 · 2021-10-23T23:15:31+0000

9514 1404 393

Answer:

20x^26

Explanation:

The leading term is the one with the highest degree.

In the expansion of (x-2)^15, that will be x^15.

In the expansion of (4-x)^11, that will be (-x)^11 = -x^11.

So, the leading term of the product is ...

(-20)(x^15)(-x^11) = 20x^26

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In the attached, terms are listed in order of increasing degree, so the "leading" term appears last.