Question

Factor the expression shown below completely.

18x^2 - 60x +50

A) 6(3x-5)^2
B) 2(6x-5)^2
C) 2(3x-5)^2
D) 3(2x-5)^2

Answer 1

`\textsf{C)} \quad 2(3x-5)^2`

Explanation:

Given quadratic:

`18x^2-60x+50`

Factor out the common term 2:

`\implies 2(9x^2-30x+25)`

To factor a quadratic in the form
`ax^2+bx+c`, find two numbers that multiply to
`ac` and sum to
`b`.

`\implies ac=9 \cdot 25=225`

`\implies b=-30`

Therefore, the two numbers are: -15 and -15.

Rewrite
`b` as the sum of these two numbers:

`\implies 2(9x^2-15x-15x+25)`

Factor the first two terms and the last two terms separately:

`\implies 2(3x(3x-5)-5(3x-5))`

Factor out the common term (3x - 5):

`\implies 2(3x-5)(3x-5)`

Apply the exponent rule aa=a²:

`\implies 2(3x-5)^2`