Factor 4x^2-9x+5

Problem

4*x2−9*x+5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=4 b=−9 and c=5

2. Find two numbers that multiply to a⋅c=4⋅5=20 and add to b=−9

3. Determine the factors of 20 that satisfy the condition. The numbers are −4 and −5 because (−4)⋅(−5)=20 and (−4)+(−5)=−9

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

5. Factor by grouping the terms: (4*x2−4*x)+(−5*x+5)

6. Factor out the greatest common factor from each group: 4*x*(x−1)−5*(x−1)

7. Extract the common binomial factor (x−1) to obtain the final factored form.

Final Answer

4*x2−9*x+5=(4*x−5)*(x−1)

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