Learning Resources

The Rational Roots Theorem

Answers to Activities Questions

1. (a) Quotient = 4x² - 9x + 12 ; Remainder = -14

4x³ - 5x² + 3x - 2 = (4x² - 9x + 12)(x + 1) - 14

(b) Quotient = x³ - x² ; Remainder = 1

x⁴ - x² + 1 = ( x³ - x² )(x + 1) + 1

(c) Quotient = x² + 3x + 2 ; Remainder = 0

x³ + x² - 4x - 4 = ( x² + 3x + 2 )( x - 2)

2. (a) (x + 2)(x + 2)

(b) (3x - 1)(2x - 3)

3. (a) {-1 , , }

(b) { -2 , - , }

(c) { , - 1 + i , - 1 - i }

(d) { - 3 , , 3i , -3i }