Example Question - polynomial expression
Here are examples of questions we've helped users solve.
Understanding and Handling a Polynomial Expression
The image shows a mathematical expression which reads: \( 64y^{10} + 17y^5 + 11 \) To "solve" this expression could mean different things depending on the context, since this is just a polynomial expression. If you're looking to simplify it, it's already in simplified form, as there are no like terms to combine. If you're trying to factor it or set it equal to something and solve for \( y \), more information or a specific instruction is needed. With the information given, there is not much else to do with the expression as it stands. If you were to set this expression equal to 0, you would be looking for the roots of the polynomial equation \( 64y^{10} + 17y^5 + 11 = 0 \), but that would generally require numerical methods or more advanced algebra to solve, as it doesn't have obvious factors that would allow for easy factoring. Please provide more specific instructions if you're looking to do something else with this expression.
Solving Indefinite Integral of Polynomial Expression
The image shows the integral of a polynomial expression. I'll guide you through the steps to solve the indefinite integral: ∫(8x^3 - x^2 + 5x - 1)dx To integrate this polynomial term by term, you would use the power rule for integration. The power rule states that the integral of x^n dx is (1/(n+1)) * x^(n+1) + C, where C is the constant of integration. Applying this rule to each term, you would get: ∫8x^3 dx = 8 * ∫x^3 dx = 8 * (1/4) * x^4 = 2x^4 ∫(-x^2) dx = (-1) * ∫x^2 dx = (-1) * (1/3) * x^3 = -1/3x^3 ∫5x dx = 5 * ∫x dx = 5 * (1/2) * x^2 = 5/2x^2 ∫(-1) dx = -1 * ∫dx = -1 * x = -x Adding them all together, you get: 2x^4 - 1/3x^3 + 5/2x^2 - x + C Therefore, the integral of the given expression is: 2x^4 - 1/3x^3 + 5/2x^2 - x + C
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