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Chapter 10: Problem 25

Combine like terms. $$2.4 x^{4}-1.6 x^{4}+5.1 x^{4}$$

Short Answer

Expert verified
The combined like terms result in 5.9 x^{4}.

Step by step solution

01

- Identify Like Terms

The expression given is 2.4x^{4}-1.6x^{4}+5.1x^{4} . Identify the like terms. In this case, all the terms have the same variable part, which is x^{4}.
02

- Combine the Coefficients

Add the coefficients of the like terms together. This means adding 2.4, -1.6, and 5.1. 2.4 + (-1.6) + 5.1 = 5.9 .
03

- Write the Combined Expression

Now, write down the combined expression. It is 5.9x^{4} .

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Key Concepts

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

Like Terms
When working with expressions and equations, identifying like terms is key.
Like terms are terms that have the same variable raised to the same power. For example, in the expression given:
  • 2.4x^{4}
  • -1.6x^{4}
  • 5.1x^{4}
All terms have the same variable part, which is x^{4}, making them like terms.
Like terms can be combined by adding or subtracting their coefficients.
Coefficients
Coefficients are the numerical part of terms that multiply the variable.
For the expression 2.4x^{4} - 1.6x^{4} + 5.1x^{4}, the coefficients are:
  • 2.4
  • -1.6
  • 5.1
To combine like terms, we add up the coefficients. In this case: 2.4 + (-1.6) + 5.1 = 5.9.
Remember that coefficients can be positive or negative, and you should carefully perform the addition or subtraction accordingly.
Polynomial
A polynomial is an expression made up of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.
The given expression, 2.4x^{4} - 1.6x^{4} + 5.1x^{4}, is an example of a polynomial.
After combining like terms, the expression simplifies to 5.9x^{4}, which is still a polynomial.
Polynomials can have multiple terms or just one term, like this simplified example.
Understanding how to work with polynomials is crucial in algebra, as it forms the basis for more complex equations and functions.

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