how do i solve 5ax^2-45a

Question

I need homework help and i don't know how to factor with more than one variable.

Answer 1

Factor with the coefficients first, then factor with the variables one at a time but you only have one variable, a ,

which is in both terms.

The GCF of 5 and 45 is 5.

The GCF of a and a is a

The GCF is 5a.

5ax^2-45a=5a(x^2-9) because 5ax^2/5a=x^2 and -45a/5a=-9

Now x^2-9 can be factored: x^2-9=(x-3)(x+3)

Answer: 5a(x-3)(x+3)

Answer 2

Hi Christian;

5ax^2-45a

Let's factor-out the a...

a(5x²-45)

Let's factor-out the 5...

5a(x²-9)

Let's factor (x²-9) into two parenthetical expressions.

For the FOIL...

FIRST must be (x)(x)=x²

OUTER and INNER must add-up to 0x or 0.

LAST must be (3)(3) and one 3 must be negative and one must be positive to render the sum of 0 and the product of -9.

5a(x-3)(x+3)

Let's FOIL...

FIRST...(x)(x)=x²

OUTER...(x)(9)=9x

INNER...(-9)(x)=-9x

LAST...(-3)(3)=-9

5a(x²+9x-9x-9)

5a(x²-9)

Answer 3

  

   5a X^2 - 45a = 0

 

   5a ( X^2 - 9 ) = 0

 

       Note : You just pull out the GCF, regardless of how many variable contains.