Algebraic division is a mathematical process used to divide two algebraic expressions, such as polynomials or rational expressions.
To solve an algebraic division question, you need to use the rules of division for algebraic expressions. These include identifying like terms, factoring, and canceling out common factors.
The steps for long division of polynomials are:
1. Write the dividend (the polynomial being divided) and the divisor (the polynomial dividing the dividend) in descending order.
2. Divide the first term of the dividend by the first term of the divisor to get the first term of the quotient.
3. Multiply the first term of the quotient by the entire divisor and write the result above the dividend.
4. Subtract this product from the first term of the dividend.
5. Bring down the next term of the dividend and repeat steps 2-4 until you have no more terms to bring down.
6. The final result is the quotient and any remaining terms are the remainder.
Synthetic division is a shortcut method for dividing polynomials by a linear binomial of the form (x - a). It is used when the divisor is of this form and can only be used to find the quotient, not the remainder.
Algebraic division has many real-life applications, such as in engineering, economics, and physics. It is used to solve equations, model real-world situations, and understand relationships between variables. For example, in finance, algebraic division can be used to calculate interest rates or determine the profitability of investments.