Which of the following cannot be a factor of x5 – ax3 + bx2 + 200?
(A) x3 – 8 (B) (x2 – 25)
(C) (x + 5) (D) (x + 15)
Answers
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)
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)