Factor 2x^2-9x+4

Problem

2*x2−9*x+4

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−9 and c=4

2. Find two numbers that multiply to a⋅c=2⋅4=8 and add to b=−9

3. Determine the factors of 8 that satisfy the condition, which are −8 and −1

4. Rewrite the middle term −9*x using these two numbers as −8*x−x

2*x2−8*x−x+4

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

2*x*(x−4)−1*(x−4)

6. Factor out the common binomial (x−4)

(2*x−1)*(x−4)

Final Answer

2*x2−9*x+4=(2*x−1)*(x−4)

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