Factor x^2-10x+21

Problem

x2−10*x+21

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−10 and c=21

2. Find two numbers that multiply to c (21 and add to b (−10.

3. Determine the factors by testing pairs of numbers that multiply to 21 (−3) and (−7)

4. Verify the sum: −3+(−7)=−10 which matches the middle coefficient.

5. Write the expression as a product of two binomials using these numbers.

Final Answer

x2−10*x+21=(x−3)*(x−7)

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