Question

if P(x) =x^3 +3x^2+2x +4, find P(4)+P(-1)+3P(0)​

Answer 1

Answer:

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Answer 2

ANSWER:

Given:

• P(x) = x³ + 3x² + 2x + 4

To Find:

• Value of P(4) + P(-1) + 3P(0)

Solution:

We are given that,

⇒ P(x) = x³ + 3x² + 2x + 4

Now, we need to find the value of,

⇒ P(4) + P(-1) + 3P(0) -----(1)

We will solve each term separately and then place them in (1).

1) P(4)

⇒ P(x) = x³ + 3x² + 2x + 4

Substituting x with 4,

⇒ P(4) = (4)³ + 3(4)² + 2(4) + 4

⇒ P(4) = 64 + 3(16) + 8 + 4

⇒ P(4) = 64 + 48 + 12

⇒ P(4) = 124

2) P(-1)

⇒ P(x) = x³ + 3x² + 2x + 4

Substituting x with -1,

⇒ P(-1) = (-1)³ + 3(-1)² + 2(-1) + 4

⇒ P(-1) = -1 + 3(1) - 2 + 4

⇒ P(-1) = -1 + 3 + 2

⇒ P(-1) = 4

3) P(0)

⇒ P(x) = x³ + 3x² + 2x + 4

Substituting x with 0,

⇒ P(0) = (0)³ + 3(0)² + 2(0) + 4

⇒ P(0) = 0 + 3(0) + 0 + 4

⇒ P(0) = 0 + 4

⇒ P(0) = 4

Now,

⇒ P(4) + P(-1) + 3P(0)

Substituting values,

⇒ (124) + (4) + 3(4)

⇒ 124 + 4 + 12

⇒ 140

Therefore, value of P(4) + P(-1) + 3P(0) is 140.