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# how do i solve 5ax^2-45a

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

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)

### Comments

Suggestion:

5 a X^2 - 5. 9 . a

GCF = 5 a    / product of common factors with lowest exponents , i.e 5and a is 5a.
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)