This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the questions. QUESTION 2 2.1 Given the expression -2x - x^3 + 9x^2 + 1. 2.1.1 How many terms does the expression consist of? The terms are -2x, -x^3, 9x^2, and 1. There are 4 terms. 4 2.1.2 What is the coefficient of x? The term containing x is -2x. The coefficient of x is -2. -2 2.1.3 What is the constant term? The constant term is the term without any variables. The constant term is 1. 1 2.1.4 Determine the value of the expression if x = -2. Step 1: Substitute x = -2 into the expression. -2(-2) - (-2)^3 + 9(-2)^2 + 1 Step 2: Calculate the powers and products. 4 - (-8) + 9(4) + 1 4 + 8 + 36 + 1 Step 3: Add the terms. 12 + 36 + 1 = 49 49 2.2 Simplify: 2.2.1 -8 - 9h + 2h + 13 Step 1: Group like terms. (-8 + 13) + (-9h + 2h) Step 2: Combine the terms. 5 - 7h 5 - 7h 2.2.2 3ab + 2a + b + a - 3b^2 - 3a - 4ba + 5b^2 - b Step 1: Identify and group like terms (ba is the same as ab). (3ab - 4ab) + (2a + a - 3a) + (b - b) + (-3b^2 + 5b^2) Step 2: Combine the like terms. -ab + 0a + 0b + 2b^2 Step 3: Simplify the expression. -ab + 2b^2 -ab + 2b^2 2.3 Simplify: 2.3.1 x^0 · x^3 Step 1: Apply the rule x^0 = 1. 1 · x^3 Step 2: Multiply. x^3 x^3 2.3.2 (n^6 m^4 · n^4 m^2)/(n^2 m^6 · n^4 m^0) Step 1: Simplify the numerator using the product rule for exponents (a^x · a^y = a^x+y). n^6+4 m^4+2 = n^10 m^6 Step 2: Simplify the denominator using the product rule for exponents and m^0 = 1. n^2+4 m^6+0 = n^6 m^6 Step 3: Divide the simplified numerator by the simplified denominator using the quotient rule for exponents ((a^x)/(a^y) = a^x-y). n^10 m^6n^6 m^6 = n^10-6 m^6-6 = n^4 m^0 Step 4: Simplify using m^0 = 1. n^4 · 1 = n^4 n^4 2.3.3 (-5x^3y^2)(3x^2y^4)(-2x) Step 1: Multiply the numerical coefficients. (-5)(3)(-2) = 30 Step 2: Multiply the x terms using the product rule for exponents. x^3 · x^2 · x^1 = x^3+2+1 = x^6 Step 3: Multiply the y terms using the product rule for exponents. y^2 · y^4 = y^2+4 = y^6 Step 4: Combine the results. 30x^6y^6 30x^6y^6 QUESTION 5 5.1 Given the expression 4x^3 - 2x^4 + 7x^2 - 5x + 13. 5.1.1 How many terms are in the given expression? The terms are 4x^3, -2x^4, 7x^2, -5x, and 13. There are 5 terms. 5 5.1.2 What is the coefficient of x^2? The term containing x^2 is 7x^2. The coefficient of x^2 is 7. 7 5.1.3 Write down the constant value. The constant term is 13. 13 5.1.4 Write the expression in a descending order form of x. Descending order means arranging terms from the highest power of x to the lowest. The powers of x are 4, 3, 2, 1, 0. -2x^4 + 4x^3 + 7x^2 - 5x + 13 -2x^4 + 4x^3 + 7x^2 - 5x + 13 5.1.5 Determine the value of the expression if x = 2. Step 1: Substitute x = 2 into the expression. 4(2)^3 - 2(2)^4 + 7(2)^2 - 5(2) + 13 Step 2: Calculate the powers. 4(8) - 2(16) + 7(4) - 5(2) + 13 Step 3: Perform the multiplications. 32 - 32 + 28 - 10 + 13 Step 4: Perform the additions and subtractions from left to right. 0 + 28 - 10 + 13 18 + 13 = 31 31 Send me the next one 📸