Factor 5x^2-14x+8

Problem

5*x2−14*x+8

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=−14 and c=8

2. Find two numbers that multiply to a⋅c=5⋅8=40 and add to b=−14

3. Determine the factors of 40 that satisfy the condition. The numbers are −10 and −4 because (−10)⋅(−4)=40 and (−10)+(−4)=−14

4. Rewrite the middle term −14*x using the two numbers found: 5*x2−10*x−4*x+8

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 5*x*(x−2)−4*(x−2)

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

Final Answer

5*x2−14*x+8=(5*x−4)*(x−2)

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