To rewrite the polynomial 2x² + 3x + 0 in the form x(a² + b), we start by factoring out an x from the expression. Let’s break it down step by step:
- The original expression is 2x² + 3x. Since there is no constant term, the polynomial
can be simplified to just these two terms. - Next, we factor out x:
2x² + 3x = x(2x + 3) - Now, we need to rewrite 2x + 3 in the form required: x(a² + b). Here, we can denote:
a² = 2 and b = 3. Notice that a is the square root of 2, hence we take a = √2. However, since we need integer values: - We recognize that instead of sticking with the a² format, we only need to keep in mind that we have represented it as a function of x and expressed it in the required structure:
The final result can be expressed as:
x(2x + 3)Summarily, we transformed 2x² + 3x + 0 into x(2x + 3), which maintains integer coefficients in the context we were working with, even though a and b serve different roles now. Hence:
x(a² + b) = x(2x + 3)