Given the expression \(5x^3+2x^2-3x+4\), is it a polynomial? If yes, factorize it.
Answer
Now, we need to factorize the polynomial. But, the polynomial \(5x^3+2x^2-3x+4\) doesn't have any common factors other than 1, and it's not a quadratic or cubic expression that can be easily factorized. Hence, the polynomial is already in its simplest form.
Step 1 ：First, we need to determine if the given expression is a polynomial. A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). Looking at our expression \(5x^3+2x^2-3x+4\), we can see that it has four terms with different powers of the same variable \(x\), hence it is a polynomial.
Step 2 ：Now, we need to factorize the polynomial. But, the polynomial \(5x^3+2x^2-3x+4\) doesn't have any common factors other than 1, and it's not a quadratic or cubic expression that can be easily factorized. Hence, the polynomial is already in its simplest form.
