Factored form of 2x^2+x-3 must show work

(2x+3)(x - 1)

Step-by-step explanation:

Since there is no common number to factor by we must approach this problem differently:

Step 1:

Multiply leading coefficient (2) by the constant term (-3)

2 x -3 = -6

Step two:

Find two numbers that multiply to -6 but add to the middle coefficient (1).

You should find these numbers to be 3 and -2

Step 3:

Replace 1x in the equation with your found numbers

2x^2 - 2x + 3x - 3

Step 4:

Take out the greatest common factor from the first two numbers, and the last two numbers.

For 2x^2 - 2x the greatest common factor would be 2x

For 3x - 3 the greatest common factor would be 3.

Step 5:

Factor out the found common factors

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

The values inside the bracket should be the same.

Step 6:

Factor out (x-1)

(x - 1)(2x + 3)

Therefore the factored form is (2x + 3)(x - 1)

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