Question

show x-3 is a factor of f(x)= x^3+x^2-17x+15

Answer 1

Let x - 3 is a factor of x³ + x² - 17 x + 15
Then x - 3 = 0
x = 3

Substitute the value in x³ + x² - 17 x + 15
then
3³ + 3² - 17*3 + 15 = 0
27 + 9 - 51 + 15 = 0
51 - 51 =0
0 = 0

Hence it is a factor

Answer 2

Hello friend,

Here's your answer:
(x - a) if a factor of f(x), then f(a) = 0.

Here x - 3 is a factor of f(x).
Where f(x) = x³ + x² - 17x + 15.
So As x - 3 = 0
=> x = 3.

Therefore 
f(3) = 3³ + 3² - 17×x + 15
=> 27 + 9 - 51 + 15
=> 51 - 51
=> 0
f(3) = 0.

Hence proved that x - 3 is a factor of x³ + x² - 17x + 15

Hope my answer helped you.

Harith
Maths Aryabhatta
Brainly Star