Factor 3x^2 + x - 4
Help?
only possible choices at the front
(3x .....)(x ......)
for each of those, choices at the back
(..... +4)(.....-1)
(..... -4)(..... +1)
(..... +2)(..... -2)
(...... -2)(..... +2)
try them
You should really learn one or more of the standard ways to factor trinomials.
Surely one has been taught to you in class.
here is a quick way to check
1. multiply the first and last coefficients ----- (3)(-4) = -12
2. look at the coefficient of the middle term ----- +1
3. what are factors of -12 that have a sum of +1 ???
I would "guess" at +4 and -3
(+4) + (-3) = 1
(4)(-3) = -12
So it does factor!
(3x +4)(x-1)
3 and 4 differ by one and you need one :)
Thank you
To factor the quadratic expression 3x^2 + x - 4, you can use either the factoring by grouping method or the quadratic formula. Let's use the factoring by grouping method.
Step 1: Multiply the coefficient of the quadratic term (3) by the constant term (-4). In this case, 3 * (-4) = -12.
Step 2: Now, find two numbers that multiply to give -12 and add up to the coefficient of the linear term (1). The numbers in this case are 4 and -3 (-3 * 4 = -12 and -3 + 4 = 1).
Step 3: Rewrite the middle term (1x) using these two numbers. We split the middle term using the numbers 4 and -3 as follows: 3x^2 + 4x - 3x - 4.
Step 4: Factor by grouping. Group the terms and factor out common factors. In this case, we can factor out "x" from the first group and factor out "1" from the second group:
x(3x + 4) - 1(3x + 4).
Step 5: Notice that we have a common binomial factor, (3x + 4), which can be factored out:
(3x + 4) (x - 1).
Therefore, the fully factored form of 3x^2 + x - 4 is (3x + 4) (x - 1).