Question

One factor of the function f(x) = x3 − 7x2 + 14x − 8 is (x − 4). Describe how to find the x-intercepts and the y-intercept of the graph of f(x). Show your work and include all intercepts in your answer.

Answer 1

Answer:

Step-by-step explanation:

x-4=0

x=4

i solve by synthetic division.

4| 1  -7   14   -8

 |     4  -12    8

 ___________

 | 1  -3    2   | 0

$x^3-7x^2+14x-8=(x-4)(x2-3x+2)\\=(x-4)[x^2-x-2x+2]\\=(x-4)[x(x-1)-2(x-1)]\\=(x-4)(x-1)(x-2)$

x-intercepts are (4,0),(1,0),(2,0)

put x=0

y=-8

y -intercept is (0,-8)