The answer is:
(x – 3)(2x + 1)
2x² - 5x – 3 = 0
The first term is, 2x² its coefficient is 2.
The middle term is, -5x its coefficient is -5.
The last term, "the constant", is -3.
Step-1: Multiply the coefficient of the first term by the constant
2 * -3 = -6
Step-2: Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5.
-6 + 1 = -5
Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 1.
2x² - 6x + 1x – 3
Step-4: Add up the first 2 terms, pulling out like factors:
2x * (x-3)
Add up the last 2 terms, pulling out common factors:
1 * (x-3)
Step-5: Add up the four terms of step 4:
(2x+1) * (x-3)
Answer: (x - 3)(2x + 1) = 0
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