Factor y^2+7y+12

Problem

y2+7*y+12

Solution

1. Identify the coefficients of the quadratic expression in the form a*y2+b*y+c where a=1 b=7 and c=12

2. Find two numbers that multiply to the constant term c=12 and add to the linear coefficient b=7

3. Determine the factors of 12 (1,12) (2,6) and (3,4)

4. Select the pair (3,4) because 3 + 4 = 7a*n*d \cdot 4 = 12$.

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

Final Answer

y2+7*y+12=(y+3)*(y+4)

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