(2x - __)(x + __) = __x² + 5x - 3
Step 1: Compare with standard form
(2x + a)(x + b) = 2x² + (2b + a)x + ab
We want: 2x² + 5x - 3
So ab = -3
2b + a = 5
Step 2: Find integers that work
Possible pairs for ab = -3: (-1,3), (1,-3), (-3,1), (3,-1)
Check which pair satisfies 2b + a = 5:
a = 3, b = -1 2(-1) + 3 = 1
a = -3, b = 1 2(1) + (-3) = -1
a = 1, b = -3 2(-3) + 1 = -5
a = -1, b = 3 2(3) + (-1) = 5
Step 3: Fill in blanks
(2x - 1)(x + 3) = 2x² + 5x - 3
Answer:
(2x - 1)(x + 3) = 2x² + 5x - 3