(v) x^3 − 2 x^2 +x−1(vi)ex+e−x
(vii) x^2 − 3 x+ 2 = 0 (viii) 2√
x−x^2
(ix)2
x+ 1(x) sinx−3cosx(xi) s1(^3) − 2 s^2 +s= 0 (xii)
4 x+ 1
x^2 − 2 x+ 4
(xiii) 2 cosx= 1 (xiv) u^2 + 2 uv− 3 v
(xv)
x−y
x+y
= 0 (xvi) xlnx+x^2 = 0
B.Identify the algebraic equations inA.
C.For each of the pair of expressions, insert brackets in the one on the left to make it
identically equal to the one on the right:
(i) a+bc+da+bc+bd (vii) x^2 − 3 x+ 4 x^2 − 3 x− 12
(ii) a+bc+dac+bc+d (viii) a+bc+bd a+bc+b^2 d
(iii) a+bc+dac+bc+ad+bd (ix) a+bc+bd ad+bcd+bd
(iv) a−bc+da−bc−bd (x) a−bc−dac−bc−ad+bd
(v) a−bc−dac−bc−d (xi) a−bc−da−bc+bd
(vi) a−bc+dac−bc+d (xii) x^2 − 3 x+ 4 x^3 − 3 x+ 4
D.Remove the brackets in the following expressions:
(i) 2(x+ 2 ) (ii) 3(x− 1 )−(x− 4 )
(iii) 3t(t− 1 ) (iv) (s−t)(s+ 2 t)
(v) a^2 (a− 3 ) (vi) (x^2 + 2 x− 1 )(x− 1 )
(vii) − 2 u(u^2 + 3 ) (viii) 9(x^2 − 3 )− 2 (x+ 4 )
(ix) (a^2 − 1 )(a+ 2 )− 3 (a− 3 ) (x) x(x− 1 )(x+ 2 )− 3 x^2
(xi) −(x−x^2 )(x− 2 ) (xii) −[(x^2 − 1 )(x− 2 )−(x− 3 )(x+ 2 )]
(xiii) ( 1 −t)( 1 −s)( 1 −u) (xiv) (a− 2 b)^2 −(a+ 2 b)^2
(xv) (x−y)^2 +(x+y)^2
E.Factorise each of your answers to QuestionDas far as possible.
2.3.2 Polynomials
➤➤
38 43
➤
A.Which of the following are polynomials? For those that are give the degree and list
the coefficients.
(i) t^2 −t+ 4 (ii) 0 (iii)
u+ 1
u− 1
(iv) 7t^3 − 2 t+1(v)4x^4 − 2 x^3 + 3 x−
1
x
(vi) 27x^4 − 3 x^2 + 1
(vii)
x^3 + 2 x
x
(viii) x+
√
x (ix) 3x^2 +t^3
(x) x^2 y+
√
y