Factor 5x^2-18x+9

Problem

5*x2−18*x+9

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=−18 and c=9

2. Find two numbers that multiply to a⋅c=5⋅9=45 and add to b=−18

3. Determine the pair of numbers, which are −15 and −3 since (−15)⋅(−3)=45 and −15+(−3)=−18

4. Rewrite the middle term −18*x using the two numbers found: 5*x2−15*x−3*x+9

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 5*x*(x−3)−3*(x−3)

6. Factor out the common binomial (x−3) to obtain the final factored form.

Final Answer

5*x2−18*x+9=(5*x−3)*(x−3)

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