Factor 2x² − 5x − 3
Worked out line by line the way a teacher would write it.
Answer
| Factored form | (x − 3)(2x + 1) |
Step-by-step solution
5 steps-
1 Given2 x^{2} - 5 x - 3
-
2 Split the middle term (ac method): find two numbers whose product is ac = -6 and whose sum is b = -5
When the x² term has a coefficient a other than 1, look for two numbers whose product is a·c = -6 and whose sum is b = -5. They split the middle term into two pieces, and the four terms can then be factored in pairs.
(-6) \cdot 1 = -6,\qquad (-6) + 1 = -5 -
3 Rewrite the middle term as the sum of those two terms
The two numbers add up to b, so writing the middle term as the sum of two terms does not change the expression. It just gives four terms that group in pairs.
2 x^{2} - 6 x + x - 3 -
4 Factor each pair by grouping
Take the greatest common factor out of the first two terms and out of the last two. Because of how the middle term was split, the same bracket shows up in both pieces.
2 x \left(x - 3\right) + \left(x - 3\right) -
5 Factored form\left(x - 3\right) \left(2 x + 1\right)
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