Question

PLEASE HELP ME ASAP. x^4+x^3-6x^2-14x-12=0. make a list of possible rational roots, test the possible roots until you find one that produces a remainder of 0,write the resulting cubic function,use synthetic division to find a second root that will reduce the cubic expression to a quadratic expression, use the quadratic formula to find the final two roots.

Answer 1

x^4+x^3-6x^2-14x-12=0.
make a list of possible rational roots, test the possible roots until you find one that produces a remainder of 0
write the resulting cubic function
use synthetic division to find a second root that will reduce the cubic expression to a quadratic expression,
use the quadratic formula to find the final two roots.

Answer 2

I solved the first one the root is 3
I dont know how to write it in cubic function or use synthetic division on it

Answer 3

x^4+x^3-6x^2-14x-12=0

Since you have an x^4 term, and x^3 term, and x^2 term, an x term, and a constant, you have all the digits you need to set up the synthetic division. (if you were missing, say, x^3 you would simply put a 0 placeholder)

anyway, looking at the coefficients, you have 1, 1, -6, -14, -12



set up the divisor on the outside (your root, 3)

Answer 4

Bring the first digit inside the box down (1)

Answer 5

multiply the divisor * the lower digit (3*1) and bring it to the next column

Answer 6

add down the column (3+1)

then repeat with the next column (the divisor * the lower digit, so 3*4, bring it to the next column, repeat)

since this is a root, keep going until you get to the last column, which is your remainder, which should be 0 if your calculations are correct

when you're done, look at the digits in the last row. those are the coefficients of your cubic function. ex: if you have a row of 1 2 3 4 the function is x^3 + 2x^2 + 3x + 4 (obvs. this is not your solution, just an example)