Find the coefficient of x^8 in the polynomial (x−1)(x−2)⋯⋯(x−10).

Orion Cervantes

Orion Cervantes

Answered question

2022-09-25

Find the coefficient of x 8 in the polynomial ( x 1 ) ( x 2 ) ( x 10 )

Answer & Explanation

Sarah Sutton

Sarah Sutton

Beginner2022-09-26Added 4 answers

On looking at the polynomial you should come to a conclusion that if exponent of x is 8, then x is multiplied by itself 8 times and by 2 numbers as there are 10 terms to be multiplied.
So the coefficient will be,
1.2 + 1.3 + . . . + 2.3 + 2.4 + . . . + 3.4 + 3.5 + . . . + 8.9 + 8.10 + 9.10
which is the sum of product of 2 numbers taken at a time.

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