5.5B – Dividing Polynomials

5.5B – Dividing Polynomials • Synthetic Division • ONLY if the DIVISOR is LINEAR ( • MISSING terms of the DIVIDEND MUST be represented as ZEROS. • Set Divisor (factor) = 0 and solve. Use the result (opposite of # in factor for the division. • New polynomial is one DEGREE smaller than original • Write answer in FRACTIONAL FORM • QUOTIENT +

Form of Synthetic Division Solution of Coefficients of Dividend Divisor (missing terms = 0) Coefficients of Quotient • Carry FIRST coefficient down below line • #’s BELOW line are MULTIPLIED by solution of divisor • Carry Product under next dividend coefficient • ADD #’s above the line & put SUM BELOW line Remainder

Examples: Synthetically Divide • 1. (

Evaluate a Polynomial • To evaluate a polynomial for x=# • 1) Direct Substitution • Replace all variables with the # and simplify • 2) Synthetic Substitution • Synthetically divide by the number • Missing terms of polynomial are ZEROS • REMAINDER is the value of the polynomial at a # • F(#)= remainder (#=x, remainder=y)

Examples: Evaluate with Synthetic Substitution • 1. f(x)= Eval at x=2 • 2. f(x)= find f(-1)

5.5B – Dividing Polynomials