Factor 4x^2-13x+9

Problem

4*x2−13*x+9

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=4 b=−13 and c=9

2. Find two numbers that multiply to a*c=4×9=36 and add to b=−13

3. Determine the factors of 36 that satisfy the condition, which are −4 and −9 because (−4)×(−9)=36 and (−4)+(−9)=−13

4. Rewrite the middle term −13*x using the two numbers found.

4*x2−4*x−9*x+9

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

4*x*(x−1)−9*(x−1)

6. Factor out the common binomial (x−1)

(4*x−9)*(x−1)

Final Answer

4*x2−13*x+9=(4*x−9)*(x−1)

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