Answer:
Hey katerbug !
[tex]{ \tt{f(x) = {3x}^{2} - 7x + 2}}[/tex]
• let's consider the general quadratic equations:
[tex]\dashrightarrow \: { \bf{ {x}^{2} + (sum \: of \: roots)x + (product \: of \: roots) }} \\ [/tex]
• then compare the equation with the general equation:
[tex]• \: { \tt{sum = - 7}} \\ • \: { \tt{product = (3 \times 2) = 6}}[/tex]
• therefore, factors are:
[tex] \dashrightarrow \: { \tt{factors = - 6 \: \: and \: \: - 1 }}[/tex]
• therefore, let's feed in the factors in the equation:
[tex]\dashrightarrow \: { \tt{(3 {x}^{2} - 6x) - (x + 2 )}} \\ \\ \dashrightarrow \: { \tt{ 3x(x - 2) - (x - 2)}} \\ \\ \dashrightarrow \: { \boxed{ \boxed{ \tt{ \: \: (3x - 1)(x - 2)}}}}[/tex]
Answer:
[tex](3x - 1)(x - 2)[/tex]
Step-by-step explanation:
In this quadratic equation,
Sum has to be
[tex]sum = ( - 7)[/tex]
And the product is
[tex]3 {x}^{2} - 7x + 2 \\ \\ product = 3 \times 2 \\ = 6[/tex]
So, the factors are,
[tex]factors \: = ( - 1) \: \: \: and( - 6)[/tex]
Let's Solve now,
[tex]3 {x}^{2} - 7x + 2 \\ 3 {x}^{2} - 6x - x + 2 \\ 3x(x - 2) - 1(x - 2) \\ (3x - 1)(x - 2) [/tex]
hope this helps you :-)
