If `p(x)=4x^(2)-3x+6` find :
(i) p(4) (ii) p(-5)

Answer

To solve the problem, we will evaluate the polynomial \( p(x) = 4x^2 - 3x + 6 \) for the given values of \( x \).

### Step 1: Calculate \( p(4) \)

1. Substitute \( x = 4 \) into the polynomial:
\[ p(4) = 4(4^2) - 3(4) + 6 \]

2. Calculate \( 4^2 \):
\[ 4^2 = 16 \]

3. Substitute back into the equation:
\[ p(4) = 4(16) - 3(4) + 6 \]

4. Calculate \( 4 \times 16 \):
\[ 4 \times 16 = 64 \]

5. Calculate \( -3 \times 4 \):
\[ -3 \times 4 = -12 \]

6. Now substitute these values into the equation:
\[ p(4) = 64 - 12 + 6 \]

7. Combine the terms:
\[ 64 - 12 = 52 \]
\[ 52 + 6 = 58 \]

Thus, \( p(4) = 58 \).

### Step 2: Calculate \( p(-5) \)

1. Substitute \( x = -5 \) into the polynomial:
\[ p(-5) = 4(-5^2) - 3(-5) + 6 \]

2. Calculate \( -5^2 \):
\[ -5^2 = 25 \]

3. Substitute back into the equation:
\[ p(-5) = 4(25) - 3(-5) + 6 \]

4. Calculate \( 4 \times 25 \):
\[ 4 \times 25 = 100 \]

5. Calculate \( -3 \times -5 \):
\[ -3 \times -5 = 15 \]

6. Now substitute these values into the equation:
\[ p(-5) = 100 + 15 + 6 \]

7. Combine the terms:
\[ 100 + 15 = 115 \]
\[ 115 + 6 = 121 \]

Thus, \( p(-5) = 121 \).

### Final Answers:
- \( p(4) = 58 \)
- \( p(-5) = 121 \)

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