Algebraic Division

Algebraic Division

Understanding Algebraic Division

• Algebraic division is a method that applies to polynomials and can be used to solve a variety of algebraic problems.
• Just as with numerical division, the aim is to divide one expression by another.

Polynomial Division

• If you’re faced with the problem of dividing one polynomial by another, the process is very similar to long division.
• The polynomial to be divided (dividend) is written first and is divided by the dividing polynomial (divisor).
• The result of this division process is called the quotient.

Long Division Approach

• The long division method is useful, especially when the divisor is a linear expression or quadratic expression.
• The process continues until either the remainder is zero or its degree is less than the degree of the divisor.

Synthetic Division Approach

• Synthetic Division is an alternate method to the long division approach and is typically faster and shorter.
• Synthetic division can only be used when the divisor is a linear binomial of the form (x − a).

Usefulness of Algebraic Division

• With algebraic division, you can express a rational function as a sum of other simpler functions.
• It’s also very useful for determining factors of a polynomial.
• It helps in breaking down complex problems into small solvable parts.

Finding Roots of Polynomials

• Algebraic division is a helpful tool in finding the roots of a polynomial.
• By setting up and solving an equation where the polynomial equals zero, you can find the roots.
• If the division is exactly divisible with a remainder of zero, then the divisor is a factor of the polynomial. This shows that the roots of the divisor are also roots of the dividend.

Remember that practise is key when mastering algebraic division. The more problems you solve, the more comfortable you’ll become with both methods of long and synthetic division.