The value of q such that x-3 divides the polynomial p(x)=x^3-9x^2+qx-15 exactly, is A)14 B)23 C)-20 D)18

Rishi Alvarado

Rishi Alvarado

Answered question

2023-01-18

The value of q such that x-3 divides the polynomial p ( x ) = x 3 9 x 2 + q x 15 exactly, is A)14 B)23 C)-20 D)18

Answer & Explanation

zupreisen14v

zupreisen14v

Beginner2023-01-19Added 11 answers

The right answer is B 23
We have that (x-3) divides the polynomial p ( x ) = x 3 9 x 2 + q x 15 exactly. This implies that the remainder will be zero i.e., (x-3) is a factor of p(x).
p ( 3 ) = 0 (By factor theorem)
( 3 ) 3 9 ( 3 ) 2 + q ( 3 ) 15 = 0
27 81 + 3 q 15 = 0
3 q 69 = 0
q = 69 3 = 23
Thus, the right answer is option (2).

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