VALOR NUMÉRICO DE UN POLINOMIO Super facil -Para principiantes

Summary

In this educational video, Daniel Carrión explains how to calculate the numerical value of polynomials by substituting specific values for their variables. Through several detailed examples, he demonstrates how to perform operations like multiplication, exponentiation, and addition/subtraction to simplify polynomials. The video covers polynomials with one or more variables and provides step-by-step instructions to make the process clear and accessible. Viewers are encouraged to try solving similar problems themselves, making the video a helpful resource for learning and reinforcing basic algebraic concepts.

Takeaways

• 😀 Understand how to evaluate polynomials by substituting values for variables.
• 😀 The first step in solving a polynomial is to substitute the given value of the variable into the equation.
• 😀 Always follow the order of operations (PEMDAS) when simplifying the polynomial.
• 😀 Multiplying constants and variables should be done first to simplify the expression.
• 😀 The square and cube of numbers should be calculated before performing addition or subtraction in the expression.
• 😀 In more complex polynomials, calculate powers (like squares and cubes) before proceeding with multiplication.
• 😀 When substituting negative values, remember to consider how the negative sign affects multiplication or exponentiation.
• 😀 The final result of evaluating a polynomial is the sum or difference after completing all operations.
• 😀 Always check your calculations, especially when dealing with multiple operations in a polynomial.
• 😀 The video encourages viewers to engage with the content by solving similar problems and commenting with answers.

Q & A

What is the first step in evaluating a polynomial when given a value for the variable?

The first step is to substitute the value of the variable into the polynomial equation, replacing the variable with the given number.

How do you evaluate a polynomial like 6x + 2 when x = 5?

To evaluate 6x + 2 when x = 5, substitute 5 for x. The equation becomes 6(5) + 2, which simplifies to 30 + 2, resulting in 32.

What is the process for evaluating a quadratic polynomial like 5x² + 10x - 20 when x = 3?

Substitute x = 3 into the polynomial. First, square 3 to get 9, then multiply 5 by 9, resulting in 45. Multiply 10 by 3 to get 30, then subtract 20. Finally, sum up 45 + 30 - 20 to get 55.

How do you evaluate a cubic polynomial like 10x³ + x² + 6 when x = -2?

Substitute x = -2 into the polynomial. First, calculate -2 raised to the power of 3, which equals -8. Then, calculate -2 squared, which equals 4. Now, multiply 10 by -8 to get -80. Add 4 and 6 to get 10. Finally, sum up -80 + 4 + 6 to get -70.

What does raising a number to a power mean, for example, 5³ or (-2)²?

Raising a number to a power means multiplying the number by itself a specified number of times. For example, 5³ means 5 × 5 × 5 = 125, and (-2)² means (-2) × (-2) = 4.

When given a polynomial like a³ + b² + a - 10, how do you evaluate it for a = 5 and b = 7?

Substitute a = 5 and b = 7 into the polynomial. First, calculate 5³ = 125, then 7² = 49. Substitute these values into the polynomial, resulting in 125 + 49 + 5 - 10. The final result is 169.

How do you simplify the expression 5x × -3 × 10?

To simplify 5x × -3 × 10, start by multiplying the constants 5, -3, and 10. Multiply 5 × -3 to get -15, and then multiply -15 × 10 to get -150.

What is the result of evaluating the polynomial x² + y² + 5xy for x = -3 and y = 10?

Substitute x = -3 and y = 10 into the polynomial. First, calculate (-3)² = 9 and 10² = 100. Then, calculate 5 × -3 × 10 = -150. Finally, sum 9 + 100 - 150 to get -41.

What does it mean to 'raise a number to a power' in the context of polynomials?

Raising a number to a power in the context of polynomials means multiplying the number by itself for the number of times indicated by the exponent. For example, x² means x × x, and x³ means x × x × x.

Can you explain the importance of the distributive property when evaluating polynomials like 5x × y?

The distributive property helps break down complex multiplication. For instance, in 5x × y, you multiply each part separately (in this case, 5 × x and x × y), which allows you to simplify and solve the polynomial more easily.