Mathematics: One factor of the function f(x) = x3 − 8x2 + 17x − 10 is (x − 5). describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. show your work and include all intercepts in your answer.

3+-5+9+-6= 3-5+9-6= (9+3) -5 -6= 12-5-6= 1.The final answer is 1.Hope this helps~...

One factor of the function f(x) = x3 − 8x2 + 17x - id382174178395, ooooooo828282828

prelogical

30.07.2020

x-intercepts: (1,0), (2,0), (5,0)

y-intercepts: (0,-10)

Step-by-step explanation:

One factor of the function f(x) = x^3-8x^2 + 17x-10 is (x-5).

Factor the polynomial in the following way:

$x^3-8x^2 + 17x-10\\ \\=x^3-5x^2-3x^2+15x+2x-10\\ \\=x^2(x-5)-3x(x-5)+2(x-5)\\ \\=(x-5)(x^2-3x+2)$

Now factor the quadratic in brackets:

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

Hence,

f(x)=(x-5)(x-2)(x-1)

The x-intercepts are points at which y = 0, so

$(x-5)(x-2)(x-1)=0\\ \\x-5=0\ \text{or}\ x-2=0\ \text{or}\ x-1=0\\ \\x=5\ \text{or}\ x=2\ \text{or}\ x=1$

The y-intercepts are points at which x = 0, so

$y=0^3-8\cdot 0^2+17\cdot 0-10=-10$

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