How do you factor 4xsquared plus 34x plus 42?

Answer 1

4x2 + 34x + 42

First, we can see that each term is divisible by two, so we'll factor that out:

= 2(2x2 + 18x + 21)

To further factor the remaining trinomial, we need to find two numbers whose product is equal to the product of our first and last terms' coefficent, and whose sum is equal to the end term's coefficient. In other words, we need two numbers that add up to 18, and multiply to make 42....

Factors of 42 are 2, 3 and 7. That means that our possible combinations of numbers are: 2 and 21, 6 and 7, or 3 and 14. Unfortunately, none of these can be added up to make 18, so the polynomial can not be factored any further.