Problem 99 Subtract. $$ \left(-3 x^{2}+... [FREE SOLUTION]

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Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

10 Edition

Chapter 5: Problem 99

Subtract. $$ \left(-3 x^{2}+2 x+9\right)-\left(x^{2}+5 x-4\right) $$

Short Answer

Expert verified

The result is $-4x^2 - 3x + 13$.

Step by step solution

- Distribute the negative sign

Distribute the negative sign to each term inside the parentheses of the second polynomial. This changes the signs of each term inside the second set of parentheses.\[(-3x^2 + 2x + 9) - (x^2 + 5x - 4) \]becomes\[-3x^2 + 2x + 9 - x^2 - 5x + 4\]

- Combine like terms

Combine like terms by grouping the x^2 terms, the x terms, and the constant terms together.\[(-3x^2 - x^2) + (2x - 5x) + (9 + 4)\]This simplifies to:\[-4x^2 - 3x + 13\]

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Key Concepts

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

Distributing Negative Sign

To subtract polynomials, the first important step is to distribute the negative sign through the second polynomial. This means you must multiply each term in the second polynomial by -1. For example, consider our exercise:

$ \left(-3x^{2} + 2x + 9\right) - \left(x^{2} + 5x - 4\right) $

Distribute the negative sign to each term inside the second set of parentheses. This will change the signs of each term:

$ +x^{2} $ becomes $ -x^{2} $
$ +5x $ becomes $ -5x $
$ -4 $ becomes $ +4 $

After distributing, the expression looks like this:

$ -3x^{2} + 2x + 9 - x^{2} - 5x + 4 $

Combining Like Terms

The next step is to combine like terms. Like terms have the same variable raised to the same power. In our modified expression, we have three types of terms: $x^{2}$ terms, $x$ terms, and constant terms.

First, group the like terms together:

$ -3x^{2} - x^{2} $
$ +2x - 5x $
$ +9 + 4 $

Let's combine each group:

$ -3x^{2} - x^{2} = -4x^{2} $
$ 2x - 5x = -3x $
$ 9 + 4 = 13 $

Combining these, the polynomial now looks like this:
$ -4x^{2} - 3x + 13 $

Simplifying Polynomials

Since we have combined all like terms, the last step is simply to write the final simplified polynomial. Always double-check each term to ensure everything is simplified correctly.

In our case, the final expression after combining like terms is:
$ -4x^{2} - 3x + 13 $

Remember to keep your terms in order, typically descending by the power of the variable. Start with the highest power term, then the next, and so forth. Be sure these terms are written correctly:

Highest power term $ -4x^{2} $
Linear term $ -3x $
Constant term $ 13 $

Thus, our expression is fully simplified and nothing more can be combined or factored within the standard scope of polynomial subtraction.

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91影视

Subtract. $$ \left(-3 x^{2}+2 x+9\right)-\left(x^{2}+5 x-4\right) $$

Short Answer

Step by step solution

- Distribute the negative sign

- Combine like terms

Key Concepts

Distributing Negative Sign

Combining Like Terms

Simplifying Polynomials

One App. One Place for Learning.

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