factor
5x^2-x-12
please help me
That does not factor into monomials with integers. It can be written as
5(x-1.6524..)(x+1.4524..)
okay thankya
To factor the expression 5x^2 - x - 12, we can use the factoring method. Let's break it down step by step:
Step 1: Look for the greatest common factor (GCF). In this case, there is no common factor other than 1.
Step 2: Check if it can be factored using the difference of squares, perfect square trinomial, or another factoring method. In this case, those methods do not apply.
Step 3: We need to find two binomials that multiply together to give us the original expression. The general form of these binomials is (ax + b)(cx + d), where a, b, c, and d are coefficients that we need to determine.
Step 4: The first term of the original expression is 5x^2, so it must come from the product of the first terms of the binomials. The only way to obtain 5x^2 is by multiplying 5x and x.
Step 5: The last term of the original expression is -12, so it must come from the product of the last terms of the binomials. The possible combinations of two numbers that multiply together to give -12 are: (1, -12), (-1, 12), (2, -6), (-2, 6), (3, -4), and (-3, 4).
Step 6: Look at the middle term of the original expression, which is -x. We need to determine how we can combine the terms from the binomials to obtain -x. This can be done by selecting the combination of numbers from Step 5 that adds up to -1 (since the coefficient of x is -1). In this case, (3, -4) fits the requirement.
Step 7: Plug the values we have determined into the binomial form (ax + b)(cx + d). This gives us (5x + 3)(x - 4).
So, the factored form of 5x^2 - x - 12 is (5x + 3)(x - 4).