6t^2+21t-12
Factor the expression
I don't know how to figure it out
I used the quadratic formula
for
6t^2+21t-12 = 0
t = [ -21 +/- sqrt(441+228) ]/12
= [ -21 +/- 27 ] /12
= 1/2 or -4
so
(x+4) and (2x -1) are factors
so try
3 (x+4)(2x-1)
Of course if I were a little smarter I would factor 3 out to start
3(2t+7t-4)
3 (t+4)(2t-1)
Thank you
Factor completely and then place the factors in the proper location on the grid.4y2 + 25y + 6
To factor the expression 6t^2 + 21t - 12, you can use the method called "factoring by grouping." Here's how you can do it:
Step 1: Multiply the coefficient of the quadratic term (6) with the constant term (-12). In this case, it is 6 * -12 = -72.
Step 2: Find two numbers that multiply to give you the product from step 1 and add up to the coefficient of the linear term (21). In this case, look for two numbers that multiply to -72 and add up to 21. The numbers are 24 and -3, as 24 * -3 = -72, and 24 + (-3) = 21.
Step 3: Rewrite the middle term (21t) using the two numbers found in step 2. We can rewrite it as 24t - 3t.
Now the expression becomes: 6t^2 + 24t - 3t - 12.
Step 4: Factor by grouping. Now group the terms in pairs:
(6t^2 + 24t) - (3t + 12).
Step 5: Factor out the greatest common factor from each pair:
6t(t + 4) - 3(t + 4).
Step 6: Notice that both terms in the parentheses are (t + 4). Factor out (t + 4):
(t + 4)(6t - 3).
Therefore, the factored form of the expression 6t^2 + 21t - 12 is (t + 4)(6t - 3).