Find the value of the polynomial 3x3 – 4x2 + 7x – 5, when x = 3

1.	Find the value of the polynomial 3x3 – 4x2 + 7x – 5, when x = 3 and also when x = -3.
Answer» 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

Find the value of the polynomial 3x3 – 4x2 + 7x – 5, when x = 3 and also when x = -3.

Answer»

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