Question

Hi. I need help with these questions.
See image for question.

Answer 1

• a) 3
• b) 15

Explanation:

Given

• P(x) = x³ + 4x² - 3x + 1

Find

• a) P( 1 ), b) P( - 2)

Solution

Substitute the value of x:

a) P(x) = x³ + 4x² - 3x + 1

• P(1) = 1³ + 4(1)² - 3(1) + 1 = 1 + 4 - 3 + 1 = 3
• P(1) = 3

b) P(x) = x³ + 4x² - 3x + 1

• P(-2) = (-2)³ + 4(-2)² - 3(-2) + 1 = -8 + 16 + 6 + 1 = 15
• P(-2) = 15

Answer 2

(a) P(1) = 3

(b) P(-2) = 15

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Function Notation

Explanation:

Step 1: Define

P(x) = x³ + 4x² - 3x + 1

P(1) is x = 1

P(-2) is x = -2

Step 2: Evaluate

P(1)

1. Substitute: P(1) = 1³ + 4(1)² - 3(1) + 1
2. Exponents: P(1) = 1 + 4(1) - 3(1) + 1
3. Multiply: P(1) = 1 + 4 - 3 + 1
4. Add: P(1) = 5 - 3 + 1
5. Subtract: P(1) = 2 + 1
6. Add: P(1) = 3

P(-2)

1. Substitute: P(-2) = (-2)³ + 4(-2)² - 3(-2) + 1
2. Exponents: P(-2) = -8 + 4(4) - 3(-2) + 1
3. Multiply: P(-2) = -8 + 16 + 6 + 1
4. Add: P(-2) = 8 + 6 + 1
5. Add: P(-2) = 14 + 1
6. Add: P(-2) = 15