Question

Find all the zeroes of the polynomial function f(x) = x^3-5x^2 +6x-30. If you use synthetic division, show all three lines of numbers.

plss help I asked my friends but they don't know either
homework question

Answer 1

you can see the details for synthetic division here:

https://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php

just enter your coefficients and it will show the workings

Answer 2

For x³ - 5 x² + 6 x - 30 you can use factoring by grouping:

x³ - 5 x² + 6 x - 30 = ( x³ - 5 x² ) + ( 6 x - 30 ) =

x² ∙ ( x - 5 ) + 6 ∙ ( x - 5) = ( x - 5 ) ∙ x² + ( x - 5 ) ∙ 6 =

( x - 5 ) ∙ ( x² + 6 )

Now:

Find root of x - 5

x - 5 = 0

Add 5 to both sides

x - 5 + 5 = 0 + 5

x = 5


x₁ = 5


Find roots of x² + 6

x² + 6 = 0

Subtract 6 to both sides

x² + 6 - 6 = 0 - 6

x² = - 6

Take square rot of both sides

x = ± √ ( - 6 )

x = ± √ ( - 1 ∙ 6 )

x = ± √ ( - 1 ) ∙ √6

x = ± i ∙ √6


x₂ = i ∙ √6

x₃ = - i ∙ √6


The solutions are:

x = - i ∙ √6 , x = i ∙ √6 , x = 5

Answer 3

I feel like im inputting the wrong things its a bit confusing sorry could you explain how to input

Answer 4

Thank you

Answer 5

huh? There is a box for each coefficient, and a small drop-down menu to choose + or -. Enter 3 for your degree, and just enter the numbers from your function.

If that's really too hard, then just google synthetic division examples and you will find lots of how-tos.