I cannot figure these out.Can someone Factor completely: 3x2 - x - 4
I suppose this is actually
3x^2 -x-4
If so:
(3x-4)(x+1)
Now I'd like you to look at the following website:
http://tutorial.math.lamar.edu/AllBrowsers/1314/Factoring.asp
To factor the quadratic expression 3x^2 - x - 4, here's a step-by-step explanation:
Step 1: Check if the quadratic expression can be factored using common factors. In this case, there are no common factors among the coefficients, so we need to use other factoring techniques.
Step 2: Look for two numbers whose product is equal to the product of the coefficient of the quadratic term (3) and the constant term (-4), i.e., -12. Additionally, the sum of these two numbers should be equal to the coefficient of the linear term (-1). In this case, the numbers -4 and 3 satisfy these conditions, as (-4) * (3) = -12 and (-4) + (3) = -1.
Step 3: Rewrite the quadratic expression by splitting the linear term using the two numbers found in Step 2. The expression becomes: 3x^2 - 4x + 3x - 4.
Step 4: Group the terms and factor by taking out the greatest common factor from each group. This gives us: x(3x - 4) + 1(3x - 4).
Step 5: Notice that we have a common factor, (3x - 4), that can be factored out. Thus, the expression becomes: (3x - 4)(x + 1).
So, the factored form of 3x^2 - x - 4 is (3x - 4)(x + 1).
For further understanding and more examples, you can visit the provided website: http://tutorial.math.lamar.edu/AllBrowsers/1314/Factoring.asp.