Given expression: 4m³ − 7m⁵ + 3 − 90m⁷ − 4m

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Here is the solution to the problem. Given expression: 4m³ − 7m⁵ + 3 − 90m⁷ − 4m a) Step 1: Identify the terms and their powers of m. The terms are: 4m³ (power 3) −7m⁵ (power 5) 3 (power 0, as 3 = 3m⁰) −90m⁷ (power 7) −4m (power 1) Step 2: Arrange the terms in descending order of their powers of m. The order of powers from highest to lowest is 7, 5, 3, 1, 0. So, the expression becomes: −90m⁷ − 7m⁵ + 4m³ − 4m + 3 b) Step 1: Count the number of terms in the expression. The terms are 4m³, −7m⁵, 3, −90m⁷, and −4m. There are 5 distinct terms. The number of terms is: 5 c) Step 1: Identify the highest power of the variable m in the expression. The powers of m are 3, 5, 0, 7, 1. The highest power is 7. The degree of the expression is: 7 d) Step 1: Locate the term containing m⁵. The term is −7m⁵. Step 2: Identify the numerical factor multiplying m⁵. The coefficient of m⁵ is: −7 e) A constant term is a term in an algebraic expression that has a value that does not change, as it does not contain any variables. In the given expression, the term without any variable m is 3. The constant term is: 3 f) Step 1: Substitute m = −1 into the expression 4m³ − 7m⁵ + 3 − 90m⁷ − 4m. 4(−1)³ − 7(−1)⁵ + 3 − 90(−1)⁷ − 4(−1) Step 2: Evaluate the powers of −1. (−1)³ = −1; (−1)⁵ = −1; (−1)⁷ = −1 Step 3: Substitute these values back into the expression. 4(−1) − 7(−1) + 3 − 90(−1) − 4(−1) Step 4: Perform the multiplications. −4 + 7 + 3 + 90 + 4 Step 5: Add the terms. −4 + 7 = 3; 3 + 3 = 6; 6 + 90 = 96; 96 + 4 = 100; The value of the expression when m = −1 is: 100

Given expression: 4m³ - 7m⁵ + 3 - 90m⁷ - 4m

Answers

Step-by-step solution

Part a· 2 steps

Identify the terms and their powers of $m$ .

Arrange the terms in descending order of their powers of $m$ .

Part b· 1 step5

Count the number of terms in the expression.

Part c· 1 step7

Identify the highest power of the variable $m$ in the expression.

Part d· 2 steps-7

Locate the term containing $m^5$ .

Identify the numerical factor multiplying $m^5$ .

Part e3

Part f· 5 steps100

Substitute $m = -1$ into the expression $4m^3 - 7m^5 + 3 - 90m^7 - 4m$ .

Evaluate the powers of $-1$ .

Substitute these values back into the expression.

Perform the multiplications.

Add the terms.

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