# Math

3x^3-9x^2-31x+5=0

How do I find the zeros, using synthetic division

1. 👍
2. 👎
3. 👁
1. let f(x) = 3x^3-9x^2-31x+5
f(1) = 3 - 9 - 31 + 5 ≠ 0
f(-1) ≠ 0
f(5) = 375 - 225 - 155 + 5 = 0
so x = 5 , and x-5 is a factor

I assume you know how to perform synthetic division.

You should get (x-5)(3x^2 + 6x - 1)

This quadratic produces two more zeros, use the quadratic formula to find them

1. 👍
2. 👎
2. There is a nice online calculator at

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

It will show the steps involved.

1. 👍
2. 👎

## Similar Questions

1. ### Algebra

Use synthetic division to find P(-3) for P(X)= x^4 - 2x^3 - 4x + 4 So I know how to do synthetic division and all, but I'm still somehow not coming up with the correct answer! Below is my work so far. Please help me interpret it

2. ### Algebra 2

When x² - 3x + 2k is divided by x + 2, the remainder is 7. Find the value of k. Use synthetic division to do so.

3. ### Algebra 2 help please :)

What is a cubic polynomial function in standard form with zeros 1, –2, and 2? Use synthetic division to find P(3) for P(x) = x^4 – 6x^3 – 4x^2 – 6x – 2. Divide 3x^3 + 3x^2 + 2x – 2 by x + 3 using long division. Divide

4. ### Algebra

Use synthetic division and the Remainder Theorem to find P(-5) if P(x) = -x^3 - 4x^2 + x - 2. Please help....?

1. ### Algebra2

Use synthetic division to find p(3) for p(x)=x^4-2x^3-4x+4 Show steps

2. ### colllege algebra

use synthetic division to factor x^3-2x^2-9x+18

3. ### calculus

Determine which consecutive integers the real zeros of the function are located. f(x) = 4x^4 - 16x^3 - 25x^2 + 196x -146 Is there an easier way to this besides trial and error synthetic division? Also, how do I approximate the

4. ### trig

The equation f(x) = 3x^3 + 10x^2 - 16x - 32 has a root at x = -4 a) Find the depressed equation using synthetic division and the root given. Factor out any constants that may appear. b) Factor the depressed equation (which is now

1. ### Algebra

(4x^3-9x+8x^2-18)/(x+2)-use synthetic division to divide. I set it up like this (pretend the parentheses are the synthetic division box). (-2) 4 8 -27 4 0 -27. For remainders, according to my book, we're supposed to divide the

2. ### Math

what are the similarities and differences found in long division of polynomials and synthetic division?

3. ### Functions

If f(x)=2x^4-9x^3+6x-5, then use synthetic division to find f(6) What is synthetic division? How do I solve this?

4. ### rational zeros theorem

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=25x^4+26x^3+126x^2+130x+5 Find the real zeros x= Use the real zeros to factor f f(x)=