Polynomial Long Division
When you try to factor a a polynomial, you are trying to find a divisor of the polynomial that gives a quotient (the other factor) and remainder zero. This suggests that being able to divide one polynomial by another could help factor polynomials .
Synthetic Division
Simplifies the long division process by a linear expression x - a. To use it, write the the coefficients in standard form (including zeroes). Omit all variables and exponents. For the divisor, reverse the sign (use a). This allows you to add instead of subtracting throughout the process.
Remainder Theorem
This provides a quick way to find the remainder of a polynomial long division problem
Practice Problems
1. Use polynomial long division to divide 4x2+23x-16 by x + 5. What is the quotient and remainder?
2. Is x2+1 a factor of 3x4-4x3+12x2+5 ?
3. Use synthetic division to divide X3-14x2+51x-54 by x + 2. What is the quotient and remainder?
4. The polynomial X3+7x2-38x-240 expresses the volume, in cubic inches , of the shadow box shown.
