Problem

Simplify the polynomial \(7x^4 - 5x^2 + 3x - 2x^4 + 4x^2 - 2x\) and find its leading coefficient.

Answer

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Answer

Step 3: The leading coefficient of the simplified polynomial is the coefficient of the term with the highest degree, which is 5 in this case.

Steps

Step 1 ：Step 1: Combine like terms, which means add together the coefficients of the same degree of x. So, \(7x^4 - 2x^4, -5x^2 + 4x^2\), and \(3x - 2x\)

Step 2 ：Step 2: After combining like terms, the polynomial becomes \(5x^4 - x^2 + x\)

Step 3 ：Step 3: The leading coefficient of the simplified polynomial is the coefficient of the term with the highest degree, which is 5 in this case.

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