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Chapter 0: Problem 14

Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. $$\left(8 x^{2}+7 x-5\right)-\left(3 x^{2}-4 x\right)-\left(-6 x^{3}-5 x^{2}+3\right)$$

Short Answer

Expert verified
The resulting polynomial in standard form is \(6x^3 + 10x^2 + 11x - 8\) and its degree is 3.

Step by step solution

01

Rearrange the terms

Rewrite the given expression, by changing the subtraction to addition of the additive inverse and distributing the negative signs: \[8x^2 + 7x - 5-(3x^2 - 4x)-(-6x^3 -5x^2 +3) \Rightarrow 8x^2 + 7x - 5 - 3x^2 + 4x + 6x^3 +5x^2 -3\]
02

Combine the like terms

By grouping all the terms with the similar degree of x: \[6x^3 + (8x^2 - 3x^2 + 5x^2) + (7x + 4x) - (5 +3) \Rightarrow 6x^3 + 10x^2 + 11x - 8 \]
03

Order in standard form and find the degree

The standard form of a polynomial orders the terms by the degree of x in descending order. The degree of the polynomial is the highest power of x in the polynomial. In this case, the polynomial is already in standard form: \(6x^3 + 10x^2 + 11x - 8\). The degree of this polynomial is 3, as that is the highest power of x.

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