Question

Factor 3x^2-7x+2 how?

Answer 1

Hey katerbug !

`{ \tt{f(x) = {3x}^(2) - 7x + 2}}`

• let's consider the general quadratic equations:

`\dashrightarrow \: { \bf{ {x}^(2) + (sum \: of \: roots)x + (product \: of \: roots) }} \\`

• then compare the equation with the general equation:

`• \: { \tt{sum = - 7}} \\ • \: { \tt{product = (3 * 2) = 6}}`

• therefore, factors are:

`\dashrightarrow \: { \tt{factors = - 6 \: \: and \: \: - 1 }}`

• therefore, let's feed in the factors in the equation:

`\dashrightarrow \: { \tt{(3 {x}^(2) - 6x) - (x + 2 )}} \\ \\ \dashrightarrow \: { \tt{ 3x(x - 2) - (x - 2)}} \\ \\ \dashrightarrow \: { \boxed{ \boxed{ \tt{ \: \: (3x - 1)(x - 2)}}}}`

Answer 2

`(3x - 1)(x - 2)`

Explanation:

In this quadratic equation,

Sum has to be

`sum = ( - 7)`

And the product is

`3 {x}^(2) - 7x + 2 \\ \\ product = 3 * 2 \\ = 6`

So, the factors are,

`factors \: = ( - 1) \: \: \: and( - 6)`

Let's Solve now,

`3 {x}^(2) - 7x + 2 \\ 3 {x}^(2) - 6x - x + 2 \\ 3x(x - 2) - 1(x - 2) \\ (3x - 1)(x - 2)`

hope this helps you :-)