# If one of the factors of 3x^2 + 8x - 35 is 3x - 7, how do you find the other factor?

##### 1 Answer
Feb 4, 2015

The solution is $\left(x + 5\right)$..

We want to find $a$ and $b$, so that $\left(3 x - 7\right) \left(a x + b\right) = 3 {x}^{2} + 8 x - 35$.

Let's just expand this some more:
$\left(3 x - 7\right) \left(a x + b\right) = 3 {x}^{2} \cdot a + 3 x \cdot b - 7 x \cdot a - 7 b$.

We want $3 {x}^{2} \cdot a$ to be equal to $3 {x}^{2}$, so $a$ should be equal to one. We want $- 7 b$ to be equal to $- 35$, so $b$ should be equal to $5$.
Now we need to check this solution:
$\left(3 x - 7\right) \left(a x + b\right) = \left(3 x - 7\right) \left(x + 5\right) = 3 {x}^{2} + 8 x - 35$. This is correct, so the factor we should multiply by is $\left(x + 5\right)$.