# Pre Calc (For Reiny)

posted by .

Thanks so much your method worked perfectly!
My solution was: the remaining zeros were 5+2i, 3, and -4

I have one question that's bugging me though, why is it that synthetic division did not work for me? I thought that long division and synthetic division were both interchangeable.

Use the given zero to find the remaining zeros of each function

f(x)=x^4-9x^3+7x^2-91x-348,zero 5-2i

I normally would use synthetic division with the root 5-2i bringing it down to x^3. Then synthetic with 5+2i, bring it down to a quadratic solve the quadratic then I'll have zeros, but I can't get past the 5-2i with the synthetic division. Every time I do it I can't get it to equal zero. I have done it multiple times and it won't work.

Pre Calc - Reiny, Friday, November 13, 2009 at 11:21pm
One property of complex roots is that they always come in conjugate pairs.
So if one root is 5-2i, there will be another 5+2i
so there are two factors,
(x - 5 - 2i) and (x - 5 + 2i)

I multiplied these and go
(x^2 - 10x + 29)

Now do a long division of
(x^4-9x^3+7x^2-91x-348) by (x^2 - 10x + 29)
That should leave you with a quadratic, that can be solved for 2 more roots.
Let me know if it worked for you.

## Similar Questions

1. ### Algebra

please help me with this question and check my answers. Solve the problem. A rectangle with width 2x + 5 inches has an area of 2x4 + 9x3 - 12x2 - 79x - 60 square inches. Write a polynomial that represents its length. ( I don't know …
2. ### Precalc

Hello, good afternoon. I need help with my precalc hw. we are learning about finding zeros I don't which method I should use for this problem: if i is a zero of x^3+3x^2+ix+(4+i) what do i do?
3. ### Pre Calc

I am familiar with this type of problem but can't seem to get the right answer. Use the given zero to find the remaining zeros of each function f(x)=x^4-9x^3+7x^2-91x-348,zero 5-2i I normally would use synthetic division with the root …

Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all the real zeros of the function. x^3 - 28x - 48 = 0 Value of x = -4 Please …
5. ### pre cal

Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all the real zeros of the function. x^3 - 28x - 48 = 0 Value of x = -4 Please …
6. ### algebra

p(x)=x^3+2x^2-3x+20 one of this functions zeros is -4 When using synthetic division to find all the zeros of a polynomial function, would you plug in 4 or -4 into the actual equation?
7. ### Calculus

Let f(x)=(2x^3-x^2+2x+1)/(x^2+1). What is the equation of the oblique asymptote of f(x)?
8. ### Pre-calc

Use the given zero to find the remaining zeros of the function: h(x)=x^4-15x^3+55x^2+155x-1476 Zero:5-4i I multiplied [x-(5-4i)][x-(5+4i)] and got x^2-10x+9. The example I have says to divide that by h and get a second quadratic equation …
9. ### Algebra 2 help please :)

What is a cubic polynomial function in standard form with zeros 1, –2, and 2?
10. ### Pre-Calc

A slice 1 unit thickness is removed from one see of a cube. Use the rational zeroes theorem and synthetic division to find the original dimensions of the cube, if the remaining volume is 48 cm^3 v= x^3 v=x*x*x x=(x-1)*x*x 48=(x-1)*x*x

More Similar Questions