Question

13. Factor the expression completely
5x²-30x+45

Answer 1

5(x-3)( x-3)

Explanation:

First we notice that all the factors are divisible by 5 because the ending of the coefficients is 0 or 5

5 (x² -6x+9)

5 ( x -3) ² , because x² -6x+9 = 9x-3)²

5 (x-3)( x-3)

Answer 2

5(x-3)(x-3)

Explanation:

First we can divide everything by 5:

`(5x^(2) -30x+45)/(5) = x^(2) -6x+9`

Now we find 2 numbers that multiply to give +9 and add to give -6:

This would be -3 and -3. Now we substitute these numbers inside of -6 by splitting -6x into -3x and -3x:

`x^(2) -3x-3x+9`

Now we factor the first 2 terms:

`x(x-3)`

Now we factor the last 2 terms:

`-3(x-3)`

Now we only copy one bracket and the things outside the bracket we put them into 1:

(x-3)(x-3)

Now we multiply everything by 5 :

5(x-3)(x-3)