Question

A polynomial function can be written as (x + 2)(x + 3)(x − 5). What are the x-intercepts of the graph of this function? (2, 0), (3, 0), (−5, 0) (−2, 0), (−3, 0), (5, 0) (2, 0), (3, 0), (5, 0) (−2, 0), (−3, 0), (−5, 0)

Answer 1

Answer: (-2,0)(-3.0)(5,0)

Explanation:

To find the x-intercepts of an equation you must first make the equation equal to 0 therefore, (x + 2)(x + 3)(x − 5) = 0

Then solve the equation algebraically.

All the numbers that x can be are the x intercepts, so we should first figure out what they are. In this case if x=-2. We would substitute our x values for -2 and solve.

-2+2=0

-2+3=1

-2-5=-7

0*1*-7= 0 so this is a.correct x intercept.

The same method can be used to verify the rest

Answer 2

x intercepts are (-2,0) (-3,0) and (5,0)

Explanation:

Given polynomial function is (x+2)(x+3)(x-5)

We need to find out x intercepts

To find x intercepts we set the polynomial function =0 and solve for x

(x+2)(x+3)(x-5) =0

We apply zero factor property. Set all the factors =0 and solve for x

x+2=0 , so x=-2

x+3 =0 , so x=-3

x-5=0, so x= 5

Now we write all the x intercepts in ordered form (x,0)

(-2,0) (-3,0) and (5,0)