What is the expression in factored form? 2x2+x−3
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To factor the expression 2x^2 + x - 3, we need to find two binomials that when multiplied together will result in the given expression.
The first step is to split the middle term, which is x, into two terms whose coefficients multiply to give the product of the coefficients of the first and last term. In this case, the product of the coefficients of the first and last term is 2 * (-3) = -6.
So, we need to find two numbers that add up to the coefficient of the middle term (which is 1) and multiply to give -6. The numbers that satisfy this requirement are -2 and 3, since -2 + 3 = 1 and (-2) * 3 = -6.
Now we rewrite the expression by replacing the middle term:
2x^2 - 2x + 3x - 3
Next, we group the terms:
(2x^2 - 2x) + (3x - 3)
Now, we factor out the greatest common factor (GCF) from each group:
2x(x - 1) + 3(x - 1)
Notice that both groups share the factor (x - 1). We can now factor (x - 1) out:
(x - 1)(2x + 3)
Therefore, the expression 2x^2 + x - 3, in factored form, is (x - 1)(2x + 3).