B. (i) (t+ 2 )(t+ 3 ) (ii) (t+ 1 )(t− 2 )(t+ 2 )(See Q2.3.2B(vii))
(iii) (y− 2 )(y− 3 )(y+ 1 )(y+ 2 )(See Q2.3.2B(iv))
(iv) ( 3 x− 1 )( 3 x+ 1 )(x+ 3 )(See Q2.3.2B(xv))2.3.4 Simultaneous equations
B. (i) Infinite number of solutionsx= 1 −s,y=s
(ii) No solutions
(iii) Trivial solutionx=y= 0
(iv) No solutions
(v) Infinity of solutionsu=−( 1 +s),u=s
(vi) No solutions2.3.5 Equalities and identities
A. (i) A=1,B=1,C=− 2
(ii) A=1,B=−^32 ,C=−1,D=− 1
(iii) A=4andB= 4 orA=−4andB= 4
(iv) A=6,B=1,C=2,D= 9
(v) A=^53 ,B=−^23
(vi) A=−1andB=± 2B. A=
(a+ 1 )b
b−aB=a^2 +b
a−b2.3.6 Roots and factors of a polynomial
(i) (u− 1 )(u+ 2 )(u− 2 ) (ii) (x− 1 )(x+ 2 )(x+ 3 )(iii) (t− 1 )(t+ 1 )(t+ 2 )(t− 3 ) (iv) (x− 1 )^2 (x+ 1 )
(v) (x+ 2 )(x− 3 )(x+ 4 )2.3.7 Rational functions
A.
Rational function? (a) denominator (b) numerator
(i) Yes x− 1 x+ 1
(ii) Yes x^2 − 1 x+√
2
(iii) No
(iv) Yes x^4 − 2 x+ 3 x^3 + 2 x− 1
(v) Yes x^4 + 12 x^4 − 1B. All values exceptx=1.