How do you factor 3x^2-x-4?
thanks in advance
How do you factor 3x^2-x-4?
thanks in advance
3 times what = 3? 3 of course. giving you (3x+/-a)(1x+/-b).
a and b can only be 1 and 4 or 2 and 2.
Can you take it from here?
(3x-4)(x+1)?
To factor the expression 3x^2 - x - 4, you follow these steps:
Step 1: Multiply the coefficient of x^2 (which is 3) and the constant term (which is -4). This gives you -12.
Step 2: Look for two numbers whose product is -12 and whose sum is the coefficient of x (which is -1). In this case, the numbers are -4 and 3 because -4 * 3 = -12 and -4 + 3 = -1.
Step 3: Rewrite the middle term (-x) as the sum of these two terms. Replace -x with -4x + 3x.
Now your expression becomes: 3x^2 - 4x + 3x - 4.
Step 4: Group the terms and factor by grouping.
(3x^2 - 4x) + (3x - 4)
Step 5: Factor out the greatest common factor from each group.
x(3x - 4) + 1(3x - 4)
Step 6: Notice that (3x - 4) is common to both terms. Factor it out.
(3x - 4)(x + 1)
So the factored form of 3x^2 - x - 4 is (3x - 4)(x + 1).