Find the zeros. 4x^2+35x-9=0

Question

Factor/Find the zeros.

Answer 1

With a large middle term, I get the feeling that we will have an x and 4x instead of 2x and 2x. Let's give that a shot first:

(4x )(x )

We have a -9, so one of the factors is positive and the other negative:

(4x - )(x + )

Let's try factoring a 3 and 3, and if that fails via redistributing, a 9 and 1:

(4x - 3)(x + 3)

4x² + 12x - 3x - 9

4x² + 9x - 9

Not enough x, so let's try the 1 and 9 with the 9 on the far side to give us plenty of x:

(4x - 1)(x + 9)

4x² + 36x - x - 9

4x² + 35x - 9

 

Since that does factor correctly we have:

4x - 1 = 0

and

x + 9 = 0

 

From here you just need to isolate x, and you'll have your zeros.

Answer 2

Hi Monica!

 

Notice that

 

4x²+35x-9=(4x-1)(x+9)=0. *******

 

So, 4x+1=0 and x+9=0.

 

So, x=-1/4 and x=-9.

 

 

**†**** If that step is not obvious, we can use the quadratic formula.

 

I hope this helpful.

 

Best regards!