i need to factor 2x²-x-6

try (2x - ?)(x + ?)

there are very few possibilities,

hint what two numbers multiply to get 6 ?

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To factor a quadratic expression like 2x²-x-6, you can follow these steps:

Step 1: Write down the quadratic expression in the form of ax² + bx + c. In this case, the expression is already in this form as 2x²-x-6.

Step 2: Multiply the coefficient of the x² term (a) by the constant term (c). For 2x²-x-6, the product is 2 * -6 = -12.

Step 3: Find two numbers whose product is the number obtained in Step 2 (-12) and whose sum is the coefficient of the x term (b) (-1 in this case). In this case, the two numbers are -4 and 3 since -4 * 3 = -12 and -4 + 3 = -1.

Step 4: Rewrite the expression by splitting the x term (-x) using the numbers found in Step 3. This gives us 2x² - 4x + 3x - 6.

Step 5: Group the terms in pairs and factor out any common terms. In this case, we can group the first two terms together and the last two terms together: (2x² - 4x) + (3x - 6).

Step 6: Factor out the greatest common factor from each group. The GCF of the first group is 2x, and the GCF of the second group is 3: 2x(x - 2) + 3(x - 2).

Step 7: Notice that both groups have the factor (x - 2). Factor out this common binomial factor: (x - 2)(2x + 3).

So, the factored form of the quadratic expression 2x² - x - 6 is (x - 2)(2x + 3).