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

MHB
Thread starter markosheehan
Start date Jun 16, 2016
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Algebra Division Polynomial Polynomial division

In summary, polynomial division is a method used to divide a polynomial by another polynomial. It is similar to long division in arithmetic, but instead of dividing numbers, we are dividing polynomials. This process is useful for simplifying complex expressions and solving equations. To divide polynomials using long division, we arrange the terms of the dividend and divisor in descending order of degree, and then divide and subtract until there are no more terms to bring down. The final result is the quotient and any remainder is written over the divisor as a fraction. However, it is not possible to divide a polynomial by a polynomial with a higher degree. The remainder in polynomial division is the leftover term after the division process is complete, which can be zero if the division is

Jun 16, 2016

markosheehan

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.

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Jun 16, 2016

MarkFL

Gold Member

MHB

I would use synthetic division here:

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

Thus, we may state:

\(\displaystyle x^3+(1-k^2)x+k=(x+k)(x^2-kx+1)\)

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

1. What is polynomial division?

Polynomial division is a method used to divide a polynomial (an expression with multiple terms) by another polynomial. It is similar to long division in arithmetic, but instead of dividing numbers, we are dividing polynomials.

2. Why do we need to divide polynomials?

Dividing polynomials is useful for simplifying complex expressions and solving equations. It allows us to break down a problem into smaller, more manageable parts.

3. How do you divide polynomials using long division?

To divide polynomials using long division, we first arrange the terms of the dividend (the polynomial being divided) and the divisor (the polynomial dividing the dividend) in descending order of degree. Then, we divide the first term of the dividend by the first term of the divisor and place the result above the dividend. Next, we multiply the divisor by this result and subtract it from the dividend. This process is repeated until we have no more terms to bring down from the dividend. The final result is the quotient (answer) and any remainder is written over the divisor as a fraction.

4. Can you divide a polynomial by a polynomial with a higher degree?

No, you cannot divide a polynomial by a polynomial with a higher degree. In polynomial division, the degree of the divisor must be equal to or lower than the degree of the dividend. If the degree of the divisor is higher, the division is not possible.

5. What is the remainder in polynomial division?

The remainder in polynomial division is the term left over after the division process is complete. It is written over the divisor as a fraction and is usually represented by "R". The remainder can also be zero, indicating that the division was exact and there is no leftover term.