Question

Which of the following cannot be a factor of x^5 - ax^3 + bx^2 + 200?
A) x^3 - 8 B) (x^2 - 25)
C) (x + 5) D) (x+15)

Answer 1

x + 15 can not be factor  for x⁵ - ax³  + bx²  + 200

Step-by-step explanation:

x⁵ - ax³  + bx²  + 200

x³(x² - a)  - 8(x² - 25)

= (x³ - 8) (x² - 25)

a = 25,

b = -8

(x² - 25) = (x + 5)(x - 5)

Hence (x³ - 8) , (x² - 25)  and x+ 5 are factors

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Answer 2

Given : The polynomial is x⁵ – ax³ + bx² + 200

To check : which of the following cannot be a factor of the above polynomial.

(A) (x³ - 8) (B) (x² - 25)

(B) (x + 5) (D) (x + 15)

solution : concept : if (x - h) is a factor of a₁xⁿ + a₂xⁿ¯¹ + a₃xⁿ¯³ + .... + a_n , then h must be a factor of a_n.

for example, (x - 5) is factor of (x³ - 125) , here we see 5 is a factor of 125.

let's come to the point !

from the above concept,

(x³ - 8) can be a factor of given polynomial because 8 is a factor of 200.

(x² - 25) can also be a factor of the polynomial because 25 is a factor of 200 too.

(x + 5) has the same explanation, it can be a factor of the polynomial.

but (x + 15) can't be a factor of the polynomial because 15 isn't a factor of 200.

Therefore the correct option is (D) (x + 15)