How do i factor 9t^2+5t-4 using the "ac" method?
I love the AC method because it gives rules to follow.
1) Take out the common factor. There is none here.
2) multiply a times c which is 9 times -4 = -36
3) Find factors of -36 that will add up to 5
2 times -18 adds to -16 NO
4 times - 9 adds to -5 NO
-4 times 9 adds to 5
replace 5t with -4t+ 9t
The order doesn't matter, but it is easier in the next step if you put the negative term first.
9t^2 -4t + 9t -4
I went back to the original equation and put in -4t and 9t for the 5t
Factor by grouping!
(9t^2 -4t) + (9t -4)
t(9t -4) + 1(9t-4)
I just took out what was common. It is important to write down the "1" if nothing else is common.
Now, you actually factor out the (9t-4). I tell my students that the factor that is there twice gets written down once. What is left over is the other factor. (9t-4)(t+1)
If you took out a common factor in the first step, this is where you would put it in front of the first factor.
You should always multiply these two factors as a check to be sure you did factor correctly. When you multiply you should get your original trinomial
y^3+y^2-4y-4
To factor the quadratic expression 9t^2 + 5t - 4 using the "ac" method, follow these steps:
Step 1: Identify the values of "a," "b," and "c" in the quadratic expression ax^2 + bx + c. In this case, a = 9, b = 5, and c = -4.
Step 2: Multiply the values of "a" and "c" together. In this case, a * c = 9 * -4 = -36.
Step 3: Determine two numbers that, when multiplied, give the product -36 and, when added, give the value of "b" (5). In this case, the numbers are 9 and -4, as 9 * -4 = -36 and 9 + (-4) = 5.
Step 4: Split the middle term (5t) into two terms using the numbers determined in step 3. Rewrite the middle term (5t) as the sum of 9t - 4t. Consequently, the quadratic expression becomes 9t^2 + 9t - 4t - 4.
Step 5: Group the terms into pairs and factor out the greatest common factor from each pair. In this case, we can factor out t from the first pair (9t^2 + 9t) and -4 from the second pair (-4t - 4).
Now, the expression becomes t(9t + 9) - 4( t + 1).
Step 6: Notice that the two terms in parentheses are identical, so we can factor out the common factor from them. The expression can be further simplified as follows:
t(9t + 9) - 4( t + 1) = t * 9(t + 1) - 4(t + 1)
Step 7: Finally, factor out the common factor (t + 1) from the expression:
t * 9(t + 1) - 4(t + 1) = (t + 1)(9t - 4)
Therefore, the quadratic expression 9t^2 + 5t - 4 can be factored as (t + 1)(9t - 4) using the "ac" method.