Question

How do you factor by trinomial $a^2 + 14a + 48$?

Answer 1

Hint: In order to do this question, you need to first split the 14a term such that if you multiply the split terms you get the value of 48. So you can split 14a as 6a and 8a as you know that 6 multiplied by 8 gives 48. Now you need to take out the common terms. And again you get the terms such that there is another common term. SO after you take it out as common, you get the final answer.

Complete step by step solution:
Here is the complete step by step solution.
The first step we need to do is to split the 14a term such that if we multiply the split terms we get the value of 48. So we can split 14a as 6a and 8a so 6 multiplied by 8 gives 48.
$\Rightarrow a^2 + 14a + 48$
$\Rightarrow a^2 + 6a + 8a + 48$
Now we take out a as common from the first two terms and then we take 8 as common from the next two terms. Therefore, we get
$\Rightarrow a\left( a+6\right) + 8\left( a+6 \right)$
Now we can see that the term a + 6 is common. SO we take it out to get the final answer.
$\Rightarrow \left( a+6\right) \left( a+8 \right)$
Therefore, we get the final answer of the question, how do you factor by trinomial $a^2 + 14a + 48$ as $\left( a+6\right) \left( a+8 \right)$.

Note: When you get these types of questions, the first and the foremost thing you need to do is to find the terms which are in common. You also can verify the answer by using the distribution law and multiply all terms. If the answer matches the question, then it is correct.