2. Find p(0).p(1) and p(2) for each of the following polynomials:
(1) p(y) = y-y + 1
(ii) p(t) = 2 +1 +27 -
(i) p(x) = x
(iv) p(x) = (x - 1)(x + 1)
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Answer:
(i) p(y)=y2−y+1
Solution:
p(y) = y2–y+1
∴p(0) = (0)2−(0)+1=1
p(1) = (1)2–(1)+1=1
p(2) = (2)2–(2)+1=3
(ii) p(t)=2+t+2t2−t3
Solution:
p(t) = 2+t+2t2−t3
∴p(0) = 2+0+2(0)2–(0)3=2
p(1) = 2+1+2(1)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)=x3
Solution:
p(x) = x3
∴p(0) = (0)3 = 0
p(1) = (1)3 = 1
p(2) = (2)3 = 8
(iv) P(x) = (x−1)(x+1)
Solution:
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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