Question

What is the factorization of 3x2 – 8x + 5?

(3x – 1)(x + 5)

(3x + 5)(x – 1)

(3x – 1)(x – 5)

(3x – 5)(x – 1)

Answer 1

we have

`3x^(2) -8x+5`

Equate the expression to zero to find the roots

`3x^(2) -8x+5=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`3x^(2) -8x=-5`

Factor the leading coefficient

`3(x^(2) -(8x/3))=-5`

Complete the square. Remember to balance the equation by adding the same constants to each side.

`3(x^(2) -(8x/3)+(16/9))=-5+(16/3)`

`3(x^(2) -(8x/3)+(16/9))=(1/3)`

Rewrite as perfect squares

`3(x-(4x/3))^(2)=(1/3)`

`(x-(4x/3))^(2)=(1/9)`

square roots both sides

`(x-(4)/(3))=(+/-) \sqrt{(1)/(9)}`

`x=(4)/(3)(+/-) (1)/(3)`

the roots are

`x=(4)/(3)+ (1)/(3)=(5)/(3)`

`x=(4)/(3)- (1)/(3)=(3)/(3)=1`

so

`3x^(2) -8x+5=3(x-(5)/(3))(x-1)=(3x-5)(x-1)`

therefore

the answer is the option

`(3x-5)(x-1)`