# factoring a polynomial: v^2 - 22v - 75

G

#### Guest

##### Guest
factor each polynomial completely:

. . .v^2 - 22v - 75

thanks-caron

#### stapel

##### Super Moderator
Staff member
Hint: Find factors of 75 that are 22 units apart.

Eliz.

#### jonboy

##### Full Member
Hello Caron!

Factor: $$\displaystyle \L v^2\, -\, 22v\, -\, 75$$
Ok since we have $$\displaystyle v^2$$ in our polynomial we need to think: What are two numbers that multiply to give us -75 and add up to -22? So after playing w/this a little bit you arrive at -25 and 3. Notice: 25 * -3 = -75 and -25 + (3) = -22. If we could not find these two number then we could just use the Quadratic Formula since I doubt you have learned difference of squares. Ok?

So since 3 > -25 our answer is:

$$\displaystyle \;\;\;\L (v+3) (v-25)$$

Check by FOIL:

$$\displaystyle \L \;\;\;v^2-25v+3v-75\,\to\,v^2\,-\,22v\,-\,75$$

Hope this helps.