/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 136 Evaluate. $$ -x^{2}-5 x+3, \... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 136

Evaluate. $$ -x^{2}-5 x+3, \text { for } x=-2 $$

Short Answer

Expert verified
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Step by step solution

01

- Substitute the value of x

Substitute the given value of \( x = -2 \) into the expression: \[ -x^2 - 5x + 3 \].
02

- Calculate \( -x^2 \)

Calculate \( -(-2)^2 \): \( (-2)^2= 4 \), so \( -(-2)^2 = -4 \).
03

- Calculate \( -5x \)

Calculate \( -5(-2) \): \( -5 \times -2 = 10 \).
04

- Combine all terms

Combine all the calculated terms and the constant: \( -4 + 10 + 3 = 9 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

order of operations
The order of operations is key when working with algebraic expressions.
It tells us correct sequence to perform calculations, ensuring we achieve accurate results.
The standard order can be recalled with the acronym PEMDAS:
  • P: Parentheses first
  • E: Exponents (powers and roots)
  • M/ D: Multiplication and Division (left to right)
  • A/ S: Addition and Subtraction (left to right)

For our exercise, let's apply PEMDAS step-by-step:
  • Calculate the exponent \( (-2)^2 = 4 \)
  • Apply multiplication \( -1 \times 4 = -4 \) and \( -5 \times (-2) = 10 \)
  • Finally, perform addition \( -4 + 10 + 3 = 9 \)
By systematically following PEMDAS, we accurately evaluate the given polynomial.

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Most popular questions from this chapter

What is the degree of \(\left(5 m^{5}\right)^{2} ?\)

Simplify. \(\frac{9}{2} x^{8}+\frac{1}{9} x^{2}+\frac{1}{2} x^{9}+\frac{9}{2} x+\frac{9}{2} x^{9}+\frac{8}{9} x^{2}+\frac{1}{2} x-\frac{1}{2} x^{8}\)

Use the fact that \(10^{3} \approx 2^{10}\) to estimate each of the following powers of \(2 .\) Then compute the power of 2 with a calculator and find the difference between the exact value and the approximation. $$ 2^{14} $$

To prepare for Section 5.3, review combining like terms and evaluating expressions (Sections 1.6 and 1.8). Combine like terms. $$ 9 x+2 y-x-2 y $$

To prepare for Section \(5.2,\) review operations with integers (Sections \(1.5-1.7)\) Perform the indicated operations. $$ -3+(-11) $$
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