EXAMPLE 3 Use synthetic division Divide f (x)= 2x3 + x2 – 8x + 5 by x + 3 using synthetic division. SOLUTION –3 2 1 –8 5 –6 15 –21 2 –5 7 –16 2x3 + x2 – 8x + 5 x + 3 = 2x2 – 5x + 7 – 16 ANSWER

EXAMPLE 4 Factor a polynomial Factor f (x) = 3x3 – 4x2 – 28x – 16 completely given that x + 2 is a factor. SOLUTION Because x + 2 is a factor of f (x), you know that f (–2) = 0. Use synthetic division to find the other factors. –2 3 –4 –28 –16 –6 20 16 3 –10 –8 0

Use the result to write f (x) as a product of two EXAMPLE 4 Factor a polynomial Use the result to write f (x) as a product of two factors and then factor completely. f (x) = 3x3 – 4x2 – 28x – 16 Write original polynomial. = (x + 2)(3x2 – 10x – 8) Write as a product of two factors. = (x + 2)(3x + 2)(x – 4) Factor trinomial.

GUIDED PRACTICE for Examples 3 and 4 Divide using synthetic division. 3. (x3 + 4x2 – x – 1)  (x + 3) x2 + x – 4 + 11 x + 3 ANSWER 4. (4x3 + x2 – 3x + 7)  (x – 1) 4x2 + 5x + 2 + 9 x – 1 ANSWER

GUIDED PRACTICE for Examples 3 and 4 Factor the polynomial completely given that x – 4 is a factor. 5. f (x) = x3 – 6x2 + 5x + 12 ANSWER (x – 4)(x –3)(x + 1) 6. f (x) = x3 – x2 – 22x + 40 ANSWER (x – 4)(x –2)(x +5)