Factor 3x^2-8x+5

Problem

3*x2−8*x+5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−8 and c=5

2. Find two numbers that multiply to a⋅c=3⋅5=15 and add to b=−8

3. Determine the two numbers, which are −3 and −5 since (−3)*(−5)=15 and −3+(−5)=−8

4. Rewrite the middle term −8*x using the two numbers found: 3*x2−3*x−5*x+5

5. Factor by grouping the first two terms and the last two terms: 3*x*(x−1)−5*(x−1)

6. Factor out the common binomial (x−1) to obtain the final factored form.

Final Answer

3*x2−8*x+5=(3*x−5)*(x−1)

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