1
Q
Factor theorem
A
If p(a)=0 (where a is a real number) then x-a is a factor of p(x)
1
Q
Remainder theorem
A
When the polynomial P(x) is divided by x-c, then the remainder is P(c), where c is a real number.
(reverse of factor theorem)
2
Q
How to do synthetic division?
A
- Given the expression to solve for, make it equal to zero and solve for x (that is what you are going to divide by)
- Set up the top row of values by inputting the coefficients and the constant of the expression - make sure to replace any missing degrees with a zero
- Move the leading coefficient to the botttom
- Multiply this number by the divisor and move the product to the second column, second row
- Add the top value with the product and bring the solution to the bottom
- Repeat this process until all places have been filled
- If the final solution does not equal zero, that is the remainder
3
Q
How to do long division?
A
- Arrange the terms in the decreasing order of their indices (if required). Write the missing terms with zero as their coefficient.
- For the first term of the quotient, divide the first term of the dividend by the first term of the divisor.
- Multiply this term of the quotient by the divisor to get the product.
- Subtract this product from the dividend, and bring down the next term (if any). The difference and the brought down term will form the new dividend.
- Follow this process until you get a remainder, which can be zero or of a lower index than the divisor.
