Factor 2x^2-9x+10

Problem

2*x2−9*x+10

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−9 and c=10

2. Find two numbers that multiply to a⋅c=20 and add to b=−9

3. Determine the pair of numbers, which are −4 and −5 since (−4)*(−5)=20 and −4+(−5)=−9

4. Rewrite the middle term −9*x using these two numbers: 2*x2−4*x−5*x+10

5. Factor by grouping the first two terms and the last two terms: 2*x*(x−2)−5*(x−2)

6. Factor out the common binomial (x−2) to obtain the final factored form.

Final Answer

2*x2−9*x+10=(2*x−5)*(x−2)

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