Q:

factor to find the zeros of 7x +14-105

Accepted Solution

A:
I'm not sure if you're asking about a linear or quadratic equation here, so I'll write about both.


y = 7x + 14 - 105

First, we need to simplify this:

y = 7x - 91

We can now pull out a greatest common factor:

y = 7(x - 13)

Now, a zero is any number x is set to that makes y equal 0.

In this case, the zero, or x-intercept, would be 13.


y = 7x² + 14x - 105

First, we should set y to 0:

7x² + 14x - 105 = 0

We can pull out a greatest common factor:

7(x² + 2x - 15) = 0

Next, we can factor it into:

7(x + 5)(x - 3) = 0

By the zero-factor property, both (x + 5) and (x - 3) are equal to zero, since their product is zero.  The numbers that would make the equation true are -5 and 3.  The zeros are -5 and 3.