Page 27 - 11-Math-4 Quadratic Equations

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Depressed Equation:

x2 + x - 2 = 0

⇒ (x + 2) (x - 1) = 0 ⇒ x = -2 or x = 1

Hence Solution set = {-2, -1, 1, 2}.

Exercise 4.5

Use the remainder theorem to find the remainder when the first polynomial is divided by
the second polynomial:

1. x2 + 3x + 7 , x + 1 2. x3 - x2 + 5x + 4 , x - 2
3. 3x4 + 4x3 + x - 5 , x + 1 4. x3 - 2x2 + 3x + 3 , x - 3

Use the factor theorem to determine if the first polynomial is a
factor of the second polynomial.

5. x - 1, x2 + 4x - 5 6. x - 2, x3 + x2 - 7x + 1

7. w + 2, 2w3 + w2- 4w + 7 8. x - a, xn - an where n is a positive

integer

9. x + a, xn + an where n is an odd integer.

10. When x4 + 2x3 + kx2 + 3 is divided by x - 2 the remainder is 1. Find the value of k.

11. When the polynomial x3 + 2x2 + kx + 4 is divided by x - 2 the remainderis 14. Find the

value of k.

Use Synthetic division to show that x is the solution of the polynomial and use the
result to factorize the polynomial completely.
12. x3 - 7x +=6 0, =x 2 13. x3 - 28x - 48 =0, x =-4

14. 2x4 + 7x3 - 4x2 - 27x -18 , x =2, x =-3

15. Use synthetic division to find the values of p and q if x + 1 and x - 2 are the factors of

the polynomial x3 + px2 + qx + 6 .

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