Let us form table of values for each line and then fix the ordered pairs to be plotted.
Graph of x = -3

Points to be plotted : (-3, -2), (-3,-1), (-3, 0), (-3,1), (-3, 1), (-3, 2)
Graph of y = 3

Points to be plotted: (-2, 3), (- 1, 3), (0, 3), (1, 3), (2, 3)

\(\therefore\) The solution is (-3, 3)

(i) x²+10x + 24 = x²+ 6x + 4x + 24
= x(x + 6) + 4(x + 6)
= (x + 6)(x + 4)

(ii) z²+ 4z -12
= z²+ 6z - 2z -12
= z(z + 6) -2(z + 6)
= (z + 6)(z - 2)

(iii) p²- 6p -16 = p²- 8p + 2p -16
= p(p - 8)+2(p - 8)
= (p - 8)(p + 2)

(iv) t²+ 72 -17t = t²-17t + 72
= t²- 9t - 8t + 72
= t(t - 9) - 8 (t - 9)
= (t - 9)(t - 8)

(v) y² -16y- 80 = y² - 20y + 4y - 80
= y(y - 20) + 4 (y - 20)
= (y - 20) (y + 4)

(vi) a² + 10a - 600
= a² + 30a - 20a - 600
= a(a + 30)- 20(a + 30)
= (a + 30)(a - 20)
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We know that (x +a)(x +b)(x +c) = x³ + (a +b +c)x² + (ab +bc + ca) x +abc     .....(1)
(i) (x+5)(x+6)(x+4)
= x³ + (5 + 6 + 4) x²+ (30 + 24 + 20) x + (5)(6)(4)
= x² + 15x²+74x + 120
[Replace a by 5 b by 6 c by 4 in (1)]
(ii) (3x-1)(3x+2)(3x-4)
(3x)³+(-1+2-4)(3x)²+(-2-8+4)(3x)+(-1)(2)(-4)
= 27x³+(-3)9x²+(-6)(3x)+8
= 27x³- 27x²-18x + 8
[Repalce x by 3x, a by -1, b by 2, c by -4 in (1)]

p(x) = ax³ - 3x² + 4
When it is divided by x - 2
p(2) = a(2)³ - 3(2)² + 4
p = 8a-12 + 4
p = 8a- 8
q(x) = 2x³ - 5x + a
When it is divided by x - 2
q(2) = 2(2)³ - 5(2) + 8
q = 16-10+a
q = 6+a
Given p - 2q = 4
8a - 8 - 2 (6 + a) = 4
8a- 8 -12 -2a = 4
6a-20 = 4
6a = 24
a = 24/6 = 4
The value of a = 4

Let the length of the reactangle be '' l ''
The Breadth of the reactangle  = x + 3
Area of rectangle = Length \(\times\) breadth
x² + 7x + 12  = l (x + 3)  or 
l = \(\frac { { x }^{ 2 }+7x+12 }{ x+3 } \)
= \(\frac { \left( x+4 \right) \left( x+3 \right) }{ x+3 } =x+4\)
Length of the rectangle = x + 4

Let f(x) = 2x⁴- 6x³+3x²+3x-2
g(x) = x² –3x + 2
= x²-2x-x+2
= x(x-2)-1(x-2)
= (x-2)(x-1)
we show that f(x) is exactly divisible by (x–1) and (x–2) using remainder theorem
f(1) = 2(1)⁴-6(1)³+3(1)²+3(1)-2
= 2 – 6 + 3 + 3 – 2 = 0
f(2) = 2(2)⁴-6(2)³+3(2)²+3(2)-2
= 32 – 48 + 12 + 6 – 2 = 0
f(x) is exactly divisible by (x – 1) (x – 2)
i.e., f(x) is exactly divisible by x² –3x + 2
If p(x) is divided by (x -a) with the remainder p(a) = 0 , then (x -a) is a factor of p(x). Remainder Theorem leads to Factor Theorem.

Length of the rectangle = 3x + 2 units
Breadth of the rectangle = 3x - 2 units
Area of the rectangle = (3x + 2 ) (3x - 2)
= 9x² - 6x + 6x - 4
= 9x²- 4
When x = 20
Area of the rectangle = 9(20)2 - 4
= 9(400) - 4
= 3600 - 4 = 3596 sq.units.