How would I factor this:
x^2 - 3x - 1
usually we restrict our factors to integer values, or at worst rational numbers.
there are no rational numbers or integers
which when multiplied give me -1 and when added give me -3
so it does not factor
Thanks :)
To factor the quadratic expression \(x^2 - 3x - 1\), we need to find two binomials that, when multiplied, give us the original expression.
Here's how you can do it step by step:
Step 1: Start with the form (x + ?)(x + ?), where ? represents the unknown factors we need to find.
Step 2: The first term of each binomial will be \(x\) since we have \(x^2\) in the original expression.
Step 3: For the second term in each binomial, we need to find two numbers whose product is \(1\) (the coefficient of the constant term) and whose sum is \(-3\) (the coefficient of the linear term).
Step 4: Find the factors of \(1\) that add up to \(-3\). The factors of \(1\) are \(\pm1\) and they add up to \(0\). Unfortunately, no combination of these factors will give us \(-3\).
Step 5: Since we cannot find two numbers that satisfy the requirements in step 4, we conclude that the given quadratic expression \(x^2 - 3x - 1\) is not factorable using integers.
Therefore, the expression \(x^2 - 3x - 1\) cannot be factored further using whole numbers.