Dividing Polynomials A-APR.6 Rewrite simple rational expressions in different forms; write a(x) / b(x) in the form q(x) + r(x) / b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Dividing by a Monomial  Split up numerator  Divide each “piece” and simplify individually  Split up numerator  Divide each “piece” and simplify individually

Synthetic Division

 Steps:  Put the opposite of the constant term of the divisor in the “box”  Write coefficients in descending order beside the “box” (if missing term put 0 in its place)  Bring down the first coefficient  Multiply by the number in the “box”  Write below the next coefficient and add  Repeat steps 4 and 5  Write answer as a polynomial with one less degree  Steps:  Put the opposite of the constant term of the divisor in the “box”  Write coefficients in descending order beside the “box” (if missing term put 0 in its place)  Bring down the first coefficient  Multiply by the number in the “box”  Write below the next coefficient and add  Repeat steps 4 and 5  Write answer as a polynomial with one less degree

Synthetic Division

Long Division  Long Division: can be used to divide all polynomials  Steps:  Divide first terms of the polynomials  Multiply by the divisor  Subtract  Bring down the next term and repeat steps until there are no more terms to bring down  Long Division: can be used to divide all polynomials  Steps:  Divide first terms of the polynomials  Multiply by the divisor  Subtract  Bring down the next term and repeat steps until there are no more terms to bring down

Long Division