Question

(a) Simplify 3x (4x – 5) + 3 and find its values for (i) x = 3**(ii)** x =$\frac{1}{2}$
(b) Simplify a (a2+ a + 1) + 5 and find its value for**(i)** a = 0, (ii) a = 1 (iii) a = – 1.

Answer 1

(a) 3x (4x – 5) + 3
=3x ( 4x) – 3x( 5) +3
=12x2 – 15x + 3

(i) Putting x=3 in the equation we get
12x2 – 15x + 3
=12(32) – 15 (3) +3
= 108 – 45 + 3
= 66

(ii) Putting x=$\frac{1}{2}$ in the equation we get
12x2 – 15x + 3

= 12 ($\frac{1}{2}$)2 – 15 ($\frac{1}{2}$) + 3

= 12 ($\frac{1}{4}$) – $\frac{15}{2}$ +3

= 3 – $\frac{15}{2}$ + 3

= 6- $\frac{15}{2}$

= $\frac{(12- 15 ) }{2}$

=$\frac{ -3}{2}$

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(b) a (a2 +a +1) +5
= a $\times$ a2 + a $\times$ a + a $\times$ 1 + 5
=a3+a2+a+ 5

(i) putting a=0 in the equation we get 03+02+0+5=5

(ii) putting a=1 in the equation we get 13 + 12 + 1+5 = 1 + 1 + 1+5 = 8

(iii) Putting a = -1 in the equation we get (-1)3+(-1)2 + (-1) +5 = -1 + 1 – 1+5 = 4