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

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

$x=\frac{4}{3}(+/-) \frac{1}{3}$

the roots are

$x=\frac{4}{3}+ \frac{1}{3}=\frac{5}{3}$

$x=\frac{4}{3}- \frac{1}{3}=\frac{3}{3}=1$

so

$3x^{2} -8x+5=3(x-\frac{5}{3})(x-1)=(3x-5)(x-1)$

therefore

the answer is the option

$(3x-5)(x-1)$

Answer 2

The factored form of the expression will be (3x-5)(x-3)

Quadratic function

Given the quadratic function 3x2 – 8x + 5

Factorizing the expression will give;

3x2 – 8x + 5

= 3x^2 - 3x - 5x  + 5

Factor out the common values

= 3x(x-3) - 5(x-3)

= (3x-5)(x-3)

Hence the factored form of the expression will be (3x-5)(x-3)

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