Find p(0), p(1),𝑝(−2) for the following polynomials: (i) (𝑥) = 10𝑥−4𝑥2 -3 (ii) (𝑦) = (y + 2) (y - 2)

Solution

(i) ( )=10 −4 2 –3

p(x) = 10 −4 2 –3

When x = 0,

p(x) = p(0)

On substituting x = 0,

p(0) = 10(0)−4(0)2 –3

= 0 – 0 – 3

= – 3

When x = 1,

p(x) = p(1)

On substituting x = 1,

p(1) = 10(1)−4(1)2 –3

= 10 – 4 – 3

= 6 – 3

= 3

When x = – 2,

p(x) = p(– 2)

On substituting x = – 2,

p(– 2) = 10(– 2)−4(– 2)2 –3

= – 20 – 16 – 3

= – 36 – 3

= – 39

 (ii) ( )=(y + 2) (y – 2)

p( )=(y + 2) (y – 2)

When y = 0,

p(y) = p(0)

On substituting y = 0,

p(0) =(0 + 2) (0 – 2)

= (2)(– 2)

= – 4

When y = 1,

p(y) = p(1)

On substituting y = 1,

p(1) =(1 + 2) (1 – 2)

=(3) (– 1)

= – 3

When y = – 2,

p(y) = p(– 2)

On substituting y = – 2,

p(– 2) =(– 2 + 2) (– 2 – 2)

= (0) (– 4)

= 0

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