Problem 12
Question
Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. $$\left(18 x^{4}-2 x^{3}-7 x+8\right)-\left(9 x^{4}-6 x^{3}-5 x+7\right)$$
Step-by-Step Solution
Verified Answer
The result of the operation is \(9x^4 + 4x^3 -2x + 1\) and its degree is 4.
1Step 1: Rewrite the Equation
The given operation can be rewritten as follows for clarity: \(18x^4 - 2x^3 - 7x + 8 - 9x^4 + 6x^3 + 5x - 7\)
2Step 2: Combine Like Terms
We can combine the like terms (terms with the same degree). This leads to: \( (18x^4 - 9x^4) + (-2x^3 + 6x^3) + (-7x +5x) + (8 - 7) \)
3Step 3: Perform the Operations
Perform the operations within parentheses yielding \(9x^4 + 4x^3 -2x + 1\)
4Step 4: Identify the Degree of the Polynomial
The degree of the polynomial is the highest power of x in the equation. Thus the degree of the polynomial is 4.
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