Factor 8x^2-14x+3

Problem

8*x2−14*x+3

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=8 b=−14 and c=3

2. Find two numbers that multiply to a⋅c=8⋅3=24 and add to b=−14

3. Determine the factors of 24 that satisfy the condition. The numbers are −12 and −2

4. Rewrite the middle term −14*x using the two numbers found: −12*x−2*x

8*x2−12*x−2*x+3

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

4*x*(2*x−3)−1*(2*x−3)

6. Factor out the common binomial (2*x−3)

(4*x−1)*(2*x−3)

Final Answer

8*x2−14*x+3=(4*x−1)*(2*x−3)

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