Algebraic Expressions And Polynomials — Important Questions

6x³ - 15x² + 12x

Step 1: Use the distributive property to multiply 3x by each term inside the brackets. Step 2: 3x × 2x² = 3 × 2 × x × x² = 6x³. Step 3: 3x × (-5x) = 3 × (-5) × x × x = -15x². Step 4: 3x × 4 = 3 × 4 × x = 12x. Step 5: Combine all terms: 6x³ - 15x² + 12x. This is the final answer.

2x² - 7

Step 1: Recall that a binomial is a polynomial with exactly two terms. Step 2: Count terms in each option: 5x has 1 term (monomial). Step 3: x² + 3x + 1 has 3 terms (trinomial). Step 4: 2x² - 7 has 2 terms (binomial). Step 5: x³ + 2x² - 5x + 3 has 4 terms. Therefore, 2x² - 7 is the binomial.

3x² + 5x - 6

Step 1: Write the subtraction as (7x² + 2x - 5) - (4x² - 3x + 1). Step 2: Distribute the negative sign: (7x² + 2x - 5) + (-4x² + 3x - 1). Step 3: Group like terms: (7x² - 4x²) + (2x + 3x) + (-5 - 1). Step 4: Simplify: 3x² + 5x - 6. This is the result of the subtraction.

-1

Step 1: Given P(x) = x² - 4x + 3, we need to find P(2). Step 2: Substitute x = 2 into the polynomial: P(2) = (2)² - 4(2) + 3. Step 3: Calculate each term: (2)² = 4, 4(2) = 8. Step 4: Substitute and simplify: P(2) = 4 - 8 + 3 = -1. Therefore, P(2) = -1.