# 6.9 Using Equations that Factor

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6.9 Using Equations that Factor

1. The product of two consecutive positive even integers is 48
1. The product of two consecutive positive even integers is 48. Find the two integers. Let n = first even integer (n + 2) = 2nd even integer n(n + 2) = 48 6 and 8 n2 + 2n = 48 n2 + 2n - 48= 0 (n + 8)(n – 6)= 0 n = -8, 6 X

2. The product of two consecutive positive odd integers is 143
2. The product of two consecutive positive odd integers is 143. Find the two integers. Let n = first odd integer (n + 2) = 2nd odd integer n(n + 2) = 143 11 and 13 n2 + 2n = 143 n2 + 2n - 143= 0 (n - 11)(n + 13)= 0 n = -13, 11 X

X (x+2)(x +6) = 60 x2 + 8x + 12 = 60 x2 + 8x - 48= 0
3. One side of a rectangle is 4 in. longer than the other. If the sides are each increased by 2 in., the area of the new rectangle is 60 in2. How long are the sides of the original rectangle? X X+4 (x+2)(x +6) = 60 x2 + 8x + 12 = 60 X+2 X+4+2 x2 + 8x - 48= 0 A = 60 in2 (x + 12)(x – 4)= 0 4 and 8 x = -12, 4 X

4. The sum of the squares of two consecutive even integers is 244
4.The sum of the squares of two consecutive even integers is 244. Find the two integers. Let n² = first consecutive square Let (n+2)² = the 2nd consecutive square (n)² +(n+2) ²=244 n² +n² +4n +4 =244 2n² +4n +4 =244 2(n²+2n +2) =244 n² +2n +2 =122 n²+2n -120 =0 (n-10) (n+12) =0 n-10 =0 or n +12 =0 If n=10 then n+2 = 12 If n =-12 then n+2 =-10 10 and 12. Also, -12 and -10

5. Fifteen more than the square of a number is eight times the number.

6. If seven is added to the square of a number, the result is 32

7. The product of two consecutive integers is 182.
13,14 and –13, -14

8. If you subtract a number from four times its square, the result is three.

9.The sum of 6 times a positive number and 1 is the same as the square of 1 less than the number.

Assignment: Page 294 (2-24) even

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