= – – = 4pt 3p –7qr – Example 2: Use long division to find ( 8 + 4x 9) ÷ (x 4). – – – 4x 12 – – 4 x – (–) 4 – + 4x –4 (–)–4 + 16x 9 –12x – (–)–12x + 48 –57 The quotient is 4x 12, and the remainder is – – –57. Therefore = 4x 12 . – – – Exercises: Simplify. 1. 2. 3. (2 5x 3) ÷ (x 3) ( 3m 7) ÷ (m + 2) 4. 5. – – – – – 6. ( 6) ÷ (p 1) 7. ( 6 + 1) ÷ (t + 2) – – – 5-2 Study Guide (continued) Synthetic Division a procedure to divide a polynomial by a binomial using coefficients of the dividend and Synthetic division the value of r in the divisor x r – Use synthetic division to find (2 5 + 5x 2) ÷ (x 1). – – – Step 1 Write the terms of the dividend so that the degrees of the terms are in 2 5 + 5x 2 – – descending Then write just the coefficients. 2 5 –5 –2
= – – = 4pt –7qr – 3p Example 2: Use long division to find ( – 8 + 4x – 9) ÷ (x – 4). – 4x – 12 x – 4 (–) – 4 –4 + 4x (–)–4 + 16x –12x – 9 (–)–12x + 48 –57 The quotient is – 4x – 12, and the remainder is –57. Therefore = – 4x – 12 – . Exercises: Simplify. 1. 2. 3. 4. (2 – 5x – 3) ÷ (x – 3) 5. ( – 3m – 7) ÷ (m + 2) 6. ( – 6) ÷ (p – 1) 7. ( – 6 + 1) ÷ (t + 2) 5-2 Study Guide (continued) Synthetic Division Synthetic division a procedure to divide a polynomial by a binomial using coefficients of the dividend and the value of r in the divisor x – r Use synthetic division to find (2 – 5 + 5x – 2) ÷ (x – 1). Step 1 Write the terms of the dividend so that the degrees of the terms are in descending Then write just the coefficients. 2 – 5 + 5x – 2 2 –5 5 –2