# Algebra2/Trig

posted by Vincent

Find all the zeros of the function and write the polynomial as a product of linear factors.

g(x)=3x^3-4x^2+8x+8

On my graphing calculator it says that it is -2/3. But when I do it by hand using synthetic division, I don't get a zero. I'm going crazy here... I've tried -2/3 and 2/3 none of them work... But when I look on my graphing calculator it says that it is -2/3. Help?

1. Reiny

if x= -2/3 then one of the factors is 3x+2

I did algebraic long division and got x^2 - 2x + 4 with no remainder.

so g(x)=3x^3-4x^2+8x+8
= (3x+2)(x^2-2x+4)
so x= -2/3 or x = 1 ± √-3 wich are complex numbers

you will not be able to express it as a product of only linear factors, but rather as a
product of a linear factor times a quadratic factor

BTW, I did get a zero when doing synthetic division.

(-2/3) │ 3 -4 8 8
********** -2 4 -8
******** 3 -6 12 0

## Similar Questions

1. ### Math (Trigenometry) 3

Write f(x)=x^4-12x^3+59x^22-138x+130 as a product of linear factors. I listed the factors of 130 and used synthetic division, but none of the remainders came out to be 0. I graphed the function, but the function doesn't pass through …
2. ### Math (Trigenometry)

Write f(x)=x^4-12x^3+59x^22-138x+130 as a product of linear factors. I listed the factors of 130 and used synthetic division, but none of the remainders came out to be 0. I graphed the function, but the function doesn't pass through …
3. ### Math (Trigenometry)

Write f(x)=x^4-12x^3+59x^2-138x+130 as a product of linear factors. I listed the factors of 130 and used synthetic division, but none of the remainders came out to be 0. I graphed the function, but the function doesn't pass through …
4. ### 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?
5. ### Trig

The polynomial function f(x) is defined by f(x)=-4x^4+9x^3+2x^2-7x-2. Use a graphing calculator to find all the points where there is a local minimum. Round to the nearest hundredth.
6. ### Algebra 2 help please :)

What is a cubic polynomial function in standard form with zeros 1, –2, and 2?
7. ### Algebra

find all zeros, write polynomial as product of linear factors 1) f(x)=9x^3 - x^2 +9x -9 2) f(x)=x^4 -21x^2 -100 3) f(x)=x^3 -3x^2 -5x +39
8. ### College Algebra

Find all the zeros of the polynomial function by using the Rational Zero Theorem, Descartes Rule of Signs and Synthetic Division. f(x)=x^3-3x^2-33x+35
9. ### algebra

Using the rational zeros theorem to find all zeros of a polynomial The function below has at least one rational zero. Use this fact to find all zeros of the function g(x)=5x©ù-28©ø-48x©÷-8x+7 if more than one zero, separate with …
10. ### algebra

Using the rational zeros theorem to find all zeros of a polynomial The function below has at least one rational zero. Use this fact to find all zeros of the function h(x)=7x^4-9x^3-41x^2+13x+6 if more than one zero, separate with commas. …

More Similar Questions