Question 1. Determine which of the following polynomials has (*x *+ 1) a factor : (i) x^{3} + x^{3} + *x *+ 1 (ii) x^{4} + x^{3} + x^{3} + *x *+ 1 (iii) x^{4} + 3x^{3} + 3x^{3} + *x *+ 1 (iv) x^{3} – x^{3} – (2+√2)*x + √*2 | |

Question 2. Use the Factor Theorem to determine whether *g*(*x*) is a factor of *p*(*x*) in each of the following cases: (i) *p*(*x*) = 2*x*^{3} + *x*^{2} – 2*x *– 1, *g*(*x*) = *x *+ 1 (ii) *p*(*x*) = *x*^{3} + 3*x*^{2} + 3*x *+ 1, *g*(*x*) = *x *+ 2 (iii) *p*(*x*) = | |

Question 3. Find the value of *k*, if *x *– 1 is a factor of *p*(*x*) in each of the following cases: (i) *p*(*x*) = *x*^{2} + *x *+ *k * (ii) *p*(*x*) = 2*x*^{2} + *kx *+ √2 (iii) *p*(*x*) = *kx*^{2} – 2*x *+ 1 (iv) *p*(*x*) = *kx*^{2} – 3*x *+ *k* | |

Question 4. Factorise : (i) 12*x*^{2} – 7*x *+ 1 (ii) 2*x*^{2} + 7*x *+ 3 (iii) 6*x*^{2} + 5*x *– 6 (iv) 3*x*^{2} – *x *– 4 | |

Questoin 5. Factorise : (i) x^{3} - 2x^{2} - x + 2 (ii) x^{3} - 3x^{2} - 9x - 5 (iii) x^{3} + 13x^{2} + 32x + 20 (iv) 2y^{3} + y^{2} - 2y - 1 | |