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Question
Find the value of the polynomial 3x3 – 4x2 + 7x – 5, when x = 3 and also when x = –3.
Solution
Given that,
p(x) = 3x3 – 4x2 + 7x – 5
According to the question,
When x = 3,
p(x) = p(3)
p(x) = 3x3 – 4x2 + 7x – 5
Substituting x = 3,
p(3) = 3(3)3 – 4(3)2 + 7(3) – 5
p(3) = 3(3)3 – 4(3)2 + 7(3) – 5
= 3(27) – 4(9) + 21 – 5
= 81 – 36 + 21 – 5
= 102 – 41
= 61
When x = –3,
p(x) = p(–3)
p(x) = 3x3 – 4x2 + 7x – 5
Substituting x = –3,
p(–3) = 3(–3)3 – 4(–3)2 + 7(–3) – 5
p(–3) = 3(–3)3 – 4(–3)2 + 7(–3) – 5
= 3(–27) – 4(9) – 21 – 5
= –81 – 36 – 21 – 5
= –143
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