How to use synthetic division and the factor theorem to determine if x - c is a factor of f(x).

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How to use synthetic division and the factor theorem to determine if x - c is a factor of f(x).

[From: ] [author: ] [Date: 11-04-23] [Hit: ]

3...8.........

anyways the final term ,in this case (-5) gives the remainder and its NOT zero, so again it proves that (x+3) is not a factor

hope that was helpful:)

-

using synthetic division

x+3=0 a=-3

-3|...3...8...-8...-20
.....,,,,,-9....3....15
-----------------------------
.......3 -1....-5...-5

by using the factor theorem

f(x)= 3x^3+8x^2-8x-20
f(-3)=3(-3)^3+8(-3)^2-8(-3)-20
=-81+72+24-20
= -5

Since f(-3) =-5, we can conclude that (x+3) is not a factor of f(x)=3x^3+8x^2-8x-20..//

-

...easiest way is to evaluate f(- 3)

if f(- 3) = 0, then (x + 3) is a factor of the polynomial using the remainder theorem...

f(- 3) = 3(- 27) + 8(9) - 8(- 3) - 20 = - 81 + 72 + 24 - 20 = - 5

(x + 3) is NOT a factor...

by synthetic division, we will have a remainder...

- 3]..3.....8.....- 8.....- 20
_______- 9___3____15
......3....- 1....- 5.....- 5

read your textbook...practice.

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