Factor 3x^2+x-2

Problem

3*x2+x−2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=1 and c=−2

2. Find two numbers that multiply to a*c=3⋅(−2)=−6 and add to b=1

3. Determine the pair of numbers, which are 3 and −2 since 3⋅(−2)=−6 and 3 + (-2) = 1$.

4. Rewrite the middle term x using these two numbers.

3*x2+3*x−2*x−2

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

3*x*(x+1)−2*(x+1)

6. Factor out the common binomial factor (x+1)

(3*x−2)*(x+1)

Final Answer

3*x2+x−2=(3*x−2)*(x+1)

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