Factor 2x^2+x-6

Problem

2*x2+x−6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=1 and c=−6

2. Find two numbers that multiply to a⋅c=2⋅(−6)=−12 and add to b=1

3. Determine the pair of numbers, which are 4 and −3 since 4⋅(−3)=−12 and 4 + (-3) = 1$.

4. Rewrite the middle term x using these two numbers as 4*x−3*x

2*x2+4*x−3*x−6

5. Factor by grouping the first two terms and the last two terms.

2*x*(x+2)−3*(x+2)

6. Factor out the common binomial factor (x+2)

(2*x−3)*(x+2)

Final Answer

2*x2+x−6=(2*x−3)*(x+2)

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