A polynomial function can be written as #(x+1)(x+4)(x-7)#. What are the #x#-intercepts of the graph of this function?

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Answer 1 · 2017-08-26T01:49:04

See a solution process below:

They #x# intercepts can be found by setting the expression to #0#:

#(x + 1)(x + 4)(x - 7) = 0#

To solve we set each term on the left side of the equation to #0# and solve for #x#:

Solution 1)

#x + 1 = 0#

#x + 1 - color(red)(1) = 0 - color(red)(1)#

#x + 0 = -1#

#x = -1# or #(-1, 0)#

Solution 2)

#x + 4 = 0#

#x + 4 - color(red)(4) = 0 - color(red)(4)#

#x + 0 = -4#

#x = -4# or #(-4, 0)#

Solution 3)

#x - 7 = 0#

#x - 7 + color(red)(7) = 0 + color(red)(7)#

#x - 0 = 7#

#x = 7# or #(7, 0)#

The x-intercepts Are: #(-1, 0)# and #(-4, 0)# and #(7, 0)#