How can I factor this:
2a^2 + 19a +42
?
I've been trying to do this for so long but I can't figure it out.
Please explain the answer as well.
The only way I can come up with is trial and error, and I've been trying so long and nothing fits..?
figured it out:
(2a+7)(a+6)
Just needed to switch the order around : )
Correct. Good job!
To factor the quadratic expression 2a^2 + 19a + 42, we can use a method called "factoring by grouping." Here's a step-by-step guide on how to do it:
Step 1: First, multiply the coefficient of the quadratic term (2) and the constant term (42). In this case, 2 * 42 = 84.
Step 2: Next, look for two numbers whose product is 84 and whose sum is the coefficient of the linear term (19). In this case, the numbers are 6 and 14. (6 * 14 = 84, 6 + 14 = 20)
Step 3: Rewrite the middle term (19a) in the quadratic expression using the two numbers from step 2. Replace the 19a term with 6a + 14a.
So, the quadratic expression 2a^2 + 19a + 42 can be written as 2a^2 + 6a + 14a + 42.
Step 4: Now, we'll factor by grouping. Group the first two terms (2a^2 and 6a) together and the last two terms (14a and 42) together.
Group 1: (2a^2 + 6a)
Group 2: (14a + 42)
Step 5: Factor out the greatest common factor from each group. In Group 1, the greatest common factor is 2a. In Group 2, the greatest common factor is 14.
Group 1: 2a(a + 3)
Group 2: 14(a + 3)
Step 6: Notice that both groups have a factor of (a + 3). Factor out (a + 3) from both groups.
Final factored form: (2a + 14)(a + 3)
So, the factored form of 2a^2 + 19a + 42 is (2a + 14)(a + 3).
If you're having trouble with trial and error, this method can be more systematic and help you find the correct factors more efficiently.