Question

hi guys please help me to solve this question please

Answer 1

We are given the polynomial:
$x^3+x^2-17x+15$

We have to find the integral zeros. 


Here, Sum of Coefficients = 1+1-17+15 = 0

So, (x-1) is a factor of the polynomial.


Now, we can factorise the polynomial as follows:

$x^3+x^2-17x+15 \\ \\ \\ = x^3 - x^2 + 2x^2 - 2x - 15x + 15 \\ \\ \\ = x^2(x-1) + 2x(x-1) -15 (x-1) \\ \\ \\ = (x-1)(x^2+2x-15) \\ \\ \\ = (x-1)(x^2+5x-3x-15) \\ \\ \\ = (x-1)(x(x+5)-3(x+5)) \\ \\ \\ = (x-1)(x+5)(x-3)$


Now, we have to find zeros:

$x^3+x^2-17x+15 = 0 \\ \\ \\ \implies (x-1)(x-3)(x+5) = 0 \\ \\ \\ \implies x-1=0 \, \, \, OR \, \, \, x-3=0 \, \, \, OR \, \, \, x+5 = 0 \\ \\ \\ \implies \boxed{x=1} \, \, \, OR \, \, \, \boxed{x=3} \, \, \, OR \, \, \, \boxed{x=-5}$


All zeros are integers. 


Thus, the integral zeros are -5, 1 and 3.



Hope it helps
Purva
Brainly Community

Answer 2

this is your answer
hope it helped
integral zeros are 3,-5,1