Question

Please factor completely:

20x^2 - 102x + 54

Answer 1

The answer to your question is 2(x - 9/2)(x - 3/5)

Explanation:

Polynomial 20x² - 102x + 54

Process

1.- Find the Greatest Common Factor

20 102 54 2

10 51 27 2

5 51 27 3

5 17 9 3

5 17 3 3

5 17 1 5

1 17 17

1

GCF = 2

2.- Factor 2

2(10x² - 51x + 27)

3.- Factor 10x² - 51x + 27

Use the general formula to solve this equation

x =
`\frac{-b +- \sqrt{b^(2) - 4ac}}{2a}`

a = 10 b = -51 c = 27

x =
`\frac{51 +- \sqrt{51^(2) -4(10)(27)}}{2(10)}`

-Simplification

x =
`(51 +- 39)/(20)`

-Result

x₁ = 9/2 x₂ = 3/5

(x - 9/2) (x - 3/5)

4.- Answer

2(x - 9/2)(x - 3/5)