MHB How can I divide a polynomial by (x+k) using synthetic division?

AI Thread Summary
To divide the polynomial x^3 + (1-k^2)x + k by (x+k) using synthetic division, the process involves setting up the synthetic division with -k as the divisor. The resulting synthetic division yields coefficients that simplify to x^2 - kx + 1. This shows that the polynomial can be expressed as x^3 + (1-k^2)x + k = (x+k)(x^2 - kx + 1). The method effectively demonstrates how to perform synthetic division with a linear binomial. Understanding this technique is crucial for polynomial division in algebra.
markosheehan
Messages
133
Reaction score
0
i am trying to divide x^3+(1-k^2)x+k by (x+k) but i can't do this can you show me how to.
 
Mathematics news on Phys.org
I would use synthetic division here:

$$\begin{array}{c|rr}& 1 & 0 & 1-k^2 & k \\ -k & & -k & k^2 & -k \\ \hline & 1 & -k & 1 & 0 \end{array}$$

Thus, we may state:

$$x^3+(1-k^2)x+k=(x+k)(x^2-kx+1)$$
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Similar threads

MHB Finding the Largest Root of a Polynomial Using Synthetic Division
Replies
1
Views
1K
B Intermediate Value Theorem and Synthetic Division
Replies
4
Views
2K
MHB Is x+1 a Factor of the Polynomial x^3-5x^2+3x+1?
Replies
2
Views
1K
MHB Question about roots/synthetic division
Replies
2
Views
2K
I Is this a proof of the Collatz Conjecture?
Replies
8
Views
3K
MHB Solve Polynomial Division: -5a + 4b = x^2+1 Rem -A-2
Replies
1
Views
1K
MHB [ASK] polynomial f(x) divided by (x - 1)
Replies
2
Views
2K
I Polynomial Division: Solve with Mike's Help!
Replies
4
Views
2K
MHB Analogy Between Long Division and Polynomial Long Division
Replies
5
Views
4K
MHB Proving Divisibility by 6 Using Mathematical Induction
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top