Factor y^2-9y+14

Problem

y2−9*y+14

Solution

1. Identify the coefficients of the quadratic expression in the form a*y2+b*y+c where a=1 b=−9 and c=14

2. Find two numbers that multiply to the constant term c=14 and add to the linear coefficient b=−9

3. Determine the factors of 14 that satisfy these conditions. The pairs of factors for 14 are (1,14) (−1,−14) (2,7) and (−2,−7)

4. Select the pair (−2,−7) because (−2)+(−7)=−9 and (−2)⋅(−7)=14

5. Write the expression in factored form (y+p)*(y+q) using the numbers found.

Final Answer

y2−9*y+14=(y−2)*(y−7)

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