Factor 3x^2-10x+8

Problem

3*x2−10*x+8

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−10 and c=8

2. Find two numbers that multiply to a⋅c=3⋅8=24 and add to b=−10

3. Determine the factors of 24 that satisfy the condition. The numbers are −6 and −4 because (−6)⋅(−4)=24 and (−6)+(−4)=−10

4. Rewrite the middle term −10*x using the two numbers found: 3*x2−6*x−4*x+8

5. Factor by grouping the first two terms and the last two terms: 3*x*(x−2)−4*(x−2)

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

Final Answer

3*x2−10*x+8=(3*x−4)*(x−2)

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