2.3 and 2.5 Polynomial Division

Possible rational zeros +- = plus or minus

6x^2 + x + 8 so possible: +-1, +-1/2, +-1/3, +-1/6, +-8, +-4, +-8/3, +-8/6, +-2, +-2/3, +-4/3

Zero Placeholders when dividing

Use 0 as a placeholder if the dividend doesn't have a term for every degree. x^3 - 1 would be x^3 + 0x^2 +0x - 1

possible rational zeros test

used to find some possible factors put all factors of the constant term over all factors of the leading coefficient

Polynomial Division Steps

1. Set up the division problem. 2. Get the first term of the quotient by dividing the leading term of the dividend by the leading term of the divisor. 3. Multiply the answer by the divisor and write it below the like terms of the dividend. 4. Subtract the bottom binomial from the terms above it. 5. Bring down the next term of the dividend. 6. Repeat steps 2-5 until reaching the last term of the dividend. 7. If the remainder is non-zero, express as a fraction using the divisor as the denominator.

synthetic division ONLY WHEN DIVISOR IS (X - K)

1. Write k for the divisor. 2. Write the coefficients of the dividend. 3. Bring the leading coefficient down. 4. Multiply the leading coefficient by k. Write the product in the next column. 5. Add the terms of the second column. 6. Multiply the result by k. Write the product in the next column. 7. Repeat steps 5 and 6 for the remaining columns. 8. Use the bottom numbers to write the quotient. The number in the last column is the remainder and has degree 0, the next number from the right has degree 1, the next number from the right has degree 2, and so on. 9. If last # is 0, then the divisor is a factor

Also use synthetic division for what

To find solve and x in an equation whatever is in the top box when plugged in the equation should equal the bottom hbox

polynomial division

follows same pattern as regular long division F(x)/ d(x) = q(x) + r(x) f(x) = dividend d(x) = divisor q(x) = quotient/answer r(x) + remainder

Tips for Polynomial Division

if ends with 0, there is no remainder and the divisor was a factor if whats left is too small to be divided it is a remainder. put it over the divisor and say remainder