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Find p(0), p(1) and p(2) for each of the following polynomials

Question

Find $p (0), p (1)$ and $p (2)$ for each of the following polynomials:
(i) $p (y) = y^{2} - y + 1$
(ii) $p (t) = 2 + t + 2 t^{2} - t^{3}$
(iii) $p (x) = x^{3}$
(iv) $p (x) = (x - 1) (x + 1)$

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Find

p (0), p (1)

and

p (2)

for each of the following polynomials:
(i)

p (y) = y^{2} - y + 1

(ii)

p (t) = 2 + t + 2 t^{2} - t^{3}

(iii)

p (x) = x^{3}

(iv)

p (x) = (x - 1) (x + 1)

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Text solutionVerified

(i)

p (y) = y^{2} - y + 1

p (0) = (0)^{2} - (0) + 1 = 0 + 0 + 1 = 1

p (1) = (1)^{2} - (1) + 1 = 1 - 1 + 1 = 1

p (2) = (2)^{2} - (2) + 1 = 4 - 2 + 1 = 3

(ii)

p (t) = 2 + t + 2 t^{2} - t^{3}

p (0) = 2 + (0) + 2 (0)^{2} - t^{3} = 2 + 0 + 0 - 0 = 2

p (1) = 2 + (1) + 2 (2)^{2} - (1)^{3} = 2 + 1 + 2 - 1 = 4

p (2) = 2 + (2) + 2 (2)^{2} - (2)^{3} = 2 + 2 + 8 - 8 = 4

(iii)

p (x) = x^{3}

p (0) = (0)^{3} = 0

p (1) = (1)^{3} = 1

p (2) = (2)^{3} = 8

(iv)

p (x) = (x - 1) (x + 1)

p (0) = (0 - 1) (0 + 1) = (- 1) (1) = - 1

p (1) = (1 - 1) (1 + 1) = (0) (2) = 0

p (2) = (2 - 1) (2 + 1) = (1) (3) = 3

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Question Text	Find $p (0), p (1)$ and $p (2)$ for each of the following polynomials: (i) $p (y) = y^{2} - y + 1$ (ii) $p (t) = 2 + t + 2 t^{2} - t^{3}$ (iii) $p (x) = x^{3}$ (iv) $p (x) = (x - 1) (x + 1)$
Answer Type	Text solution:1
Upvotes	150