Question

using factor theorem find the following 1. xcube minus6xcube plus3x plus10 ​

Answer 1

Answer:

(x+1) , (x-2) and (x-5) are factors of the given polynomial

Step-by-step explanation:

Concept used:

Factor theorem:

(x-a) is a factor of P(x) if and only if P(a)=0

Given:

$P(x)=x^3-6x^2+3x+10$

sum of the coefficients of odd powers of x = 1+3 = 4

sum of the coefficients of even powers of x = -6+10 = 4

Therefore, (x + 1) is a factor of P(x)

Put x=2 in P(x),

$P(2)=2^3-6(2)^2+3(2)+10$

$P(2)=8-24+6+10$

$P(2)=0$

By factor theorem (x-2) is a factor of P(x)

Put x=5 in P(x),

$P(5)=5^3-6(5)^2+3(5)+10$

$P(5)=125-150+15+10$

$P(5)=0$

By factor theorem (x-5) is a factor of P(x)

Answer 2

Answer:

(x+1) , (x-2) and (x-5) are factors of the given polynomial