Question

Math is uhhh confusing to me please help

Answer 1

x = 1, x = 2, x = 5

Explanation:

Divide f(x) by (x - 2) using Synthetic division

2 | 1 - 8 17 - 10

↓ 2 - 12 10

--------------------------

1 - 6 5 0 ← remainder

quotient = x² - 6x + 5 = (x - 1)(x - 5)

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

To find the zeros let f(x) = 0 , that is

(x - 1)(x - 2)(x - 5) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

x - 5 = 0 ⇒ x = 5

Answer 2

x = 1, x = 2, x = 5

Explanation:

`f(x)=x^3-8x^2+17x-10`

if
`x - 2` is a factor of
`f(x)`, then

`f(x)=(x-2)(x^2+bx+5)`

Expand brackets:

`\implies f(x)=x^3+bx^2+5x-2x^2-2bx-10`

Combine like terms:

`\implies f(x)=x^3+(b-2)x^2+(5-2b)x-10`

Compare coefficients for
`x^2`:

`b-2=-8`

`\implies b=-6`

Therefore,

`f(x)=(x-2)(x^2-6x+5)`

Factoring
`(x^2-6x+5)`:

`\implies f(x)=(x-2)(x-1)(x-5)`

To find the zeros of
`f(x)`, set the function to zero and solve for
`x`:

`\implies f(x)=0\\\\\implies(x-2)(x-1)(x-5)=0\\\\\implies x=2,x=1,x=5`