Factor 3x^2-16x+5

Problem

3*x2−16*x+5

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=3 b=−16 and c=5

2. Find two numbers that multiply to a⋅c=3⋅5=15 and add to b=−16

3. Determine the pair of numbers, which are −15 and −1

4. Rewrite the middle term −16*x using these two numbers: 3*x2−15*x−x+5

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 3*x*(x−5)−1*(x−5)

6. Factor out the common binomial (x−5) to obtain the final factored form.

Final Answer

3*x2−16*x+5=(3*x−1)*(x−5)

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