Factor n^2-8n-72

Problem

n2−8*n−72

Solution

1. Identify the coefficients of the quadratic expression in the form a*n2+b*n+c where a=1 b=−8 and c=−72

2. Find two integers that multiply to c=−72 and add to b=−8

3. List factor pairs of −72 (1,−72) (−1,72) (2,−36) (−2,36) (3,−24) (−3,24) (4,−18) (−4,18) (6,−12) (−6,12) (8,−9) (−8,9)

4. Check the sums of these pairs: 6 + (-12) = -6a*n*d + (-18) = -14.N*o*n*e*o*ƒ*t*h*e*i*n*t*e*g*e*r*ƒ*a*c*t*o*r*p*a*i*r*s(o)*ƒ72s(u)*m*t*o8$.

5. Apply the quadratic formula to find the roots if integer factoring is not possible: n=(−b±√(,b2−4*a*c))/(2*a)

6. Substitute the values: n=(8±√(,(−8)2−4*(1)*(−72)))/(2*(1))

7. Simplify the discriminant: n=(8±√(,64+288))/2

8. Simplify further: n=(8±√(,352))/2

9. Factor the radical: √(,352)=√(,16×22)=4√(,22)

10. Solve for n n=(8±4√(,22))/2=4±2√(,22)

11. Write the factored form using the roots (r_1) and (r_2) as (n−(r_1))*(n−(r_2))

Final Answer

n2−8*n−72=(n−(4+2√(,22)))*(n−(4−2√(,22)))

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