Factorizing This Algebra 1 Equation?

What two numbers multiplied together get you 3x^2? 3x and x

What two numbers multiplied together get you -2? 1 and -2 or -1 and 2

try out some options

(3x+2)(x-1) = 3x^2 + 2x -1x -2 = 3x^2-x-2 NOPE

(3x+1)(x-2) = 3x^2 - 6x + x -2 = 3x^2 - 5x - 2 NOPE, but close.

(3x-1)(x+2) = 3x^2 + 6x - x - 2 = 3x^x + 5x - 2 YES!!!!!

( 3x - 1) (x +2)

FOIL
First, outter, inner last

(3x-1)(x+2) = 3x^2 + 6x - x - 2 = 3x^x + 5x - 2

Steps are :-
(3x-----)(x------)
(3x-----1)(x----2)
(3x - 1)(x + 2)

You use FOIL to solve this problem but there's an alternative way to solve it. 3x6^2+5x-2 is set as Ax^2+Bx+C otherwise known as a quadratic equation. Take A and multiply it by C. In this case is 3 times -2 giving you -6 and that's C. The new equation is x^2+5x-6, now factor which should be easier. x^2+5x-6 = ( x+6 ) ( x-1 ), now add 3 in from off the x's, ( 3x+6 ) ( 3x-1 ) and as you can see you can simplify one of the factors. ( 3x+6 ) can be simplify into ( x+2 ). Your final result is ( x+2 ) ( 3x-1 ).

3x^2+5x-2= [ multiply 3 to -2 ]
x^2+5x-6= [ factor ]
(x+6) (x-1) [ put a 3 on front of the x's ]
(3x+6) (3x-1) [ simplify if you can and you can in this case ]
(x+2) (3x-1)

Answer- ( x+2 ) ( 3x-1 )

3x^2 + 5x - 2
= 3x^2 + 6x - x - 2
= (3x^2 + 6x) - (x + 2)
= 3x(x + 2) - 1(x + 2)
= (x + 2)(3x - 1)

__________________________
3x²+5x-2
ax²+bx+c

to factor this, you need to find 2 numbers that have
a product of ac and a sum of b.

For this problem, then, you need 2 numbers that have a product
of -6 and a sum of +5.
That would be 6 and -1.

(3x.....)(..+ 2) ... NOTE: by FOIL, Outside is 3•2 = 6
(3x - 1)(x + 2) ... NOTE: by FOIL, Inside is -1•1 = -1

This makes 5, i.e.6+(-1), the coefficient of the middle term

__________________________________________________

In this expression 3 is coefficient of x^2, sum is +5 and -2 is constant.
Product is coefficient*constant= +3*-2 = -6. While factorising we look for the factors of product -6, they are +1*-6 , -1*+6, +2*-3 and -2*+3.
Which of these factors has a sum of +5? the second one -1+6= +5.
Then we break the 5x into -1x+6x :
3x^2+5x-2
= 3x^2-1x+6x-2

from here factorise by grouping(put in brackets)
= (3x^2-1x) + (6x-2)

we remove common from each bracket:
= x(3x-1) + 2(3x-1)

u can see there are 2 brackets of (3x-1),
we make the 2 brackets into 1 and the values outside into 1 bracket:
=(3x-1) (x+2)
Here's the answer (3x-1) (x+2)