Worksheet 4.7 Polynomials

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Section 3 1. (a) 486 (b) 16 2. (a) 18 (b) 10 (c) 77 (d) 12 Section 4 1. (a) (x − 2)(x 2 − x + 3) (b) (x − 1) 2 (x + 5) 2. k = 3, roots: 2 (double), −7 3. 6x 2 + 4x − 2 4. 4x 3 − 20x 2 + 12x + 36 5. (b) 1 , −2 3 Exercises <strong>4.7</strong> 1. (a) q(x) = x − 1, r(x) = x + 2 (b) q(x) = x 2 − 2x − 6, r = 33 2. (a) (3x − 2)(x + 1)(x − 3) (b) (x − 2)(x 2 − 2x + 2) (c) x(2x − 1)(x + 3) (d) (x − 1)(x 2 + x − 2) (e) (x + 2) 3 3. (a) 2, −1+√ (b) 5 , 2 2 5 (c) 3, 2 (d) 1 , −1, −4 (e) 2, −2, −5 4. (a) a = 5 −1− √ 5 2 (b) factors are (x − 3) and (x 2 − x + 1) 10 (c) x(2x + 1)(3x − 2) (d) (4x + 1)(x − 3)(x + 1) (c) q(x) = 2x 2 − 1, r = 0 (d) q(x) = x − 1, r(x) = 4x − 5
5. (a) k = 11, factors are (x − 4), (x + 1) and (3x − 2) (b) roots are 4, −1 and 2 3 6. 5x 2 + 14x − 3 7. x 2 − 3x − 4 8. 2x 3 − 6x 2 + 2x + 2 11
Page 1 and 2: A polynomial is an expression of th
Page 3 and 4: Exercises: So 3x 3 − 2x 2 + 4x +
Page 5 and 6: Note: Checking this using long divi
Page 7 and 8: 3. Find the quadratic whose roots a
Page 9: Answers 4.7 Section 1 1. (a) (i) 1

Worksheet 4.7 Polynomials

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