Example 2. The length of a rectangle is 7 more than the width. Its area is 30. Find the dimensions of the rectangle.

A = 30 x + 7 x A = lw 30 = x(x + 7) 30 = x 2 + 7x -30 -30 0 = x 2 + 7x – 30 Use the x-box to factor the trinomial if you can’t do it in your head.

Reject -10 because you cannot have a negative dimension.

0 = x + 10 -10 -10 x – 3 = 0 +3 +3 x = 3 Answer: Length = 3 + 7 = 10 Width = 3

Example 3. Kara has two sisters. One of the sisters is 7 years older than Kara. The other sister is 3 years younger than Kara. The product of Kara's sisters' ages is 24 . How old is Kara? (Hint: let x = Kara’s age, and use the sentence in the problem to write an equation to solve.) Let: x = Kara’s age x – 3 = youngest sister’s age x + 7 = oldest sister’s age x 2 (x – 3)(x + 7) = 24 + 7x – 3x – 21 = 24 x 2 + 4x – 21 = 24 x 2 -24 -24 + 4x – 45 = 0( Answer: Kara is 5 x + 9 = 0 -9 -9 x = - 9 reject x – 5 = 0 +5 +5 x = 5

1) Let x = a number x 2 + 8 = 6x x 2 -6x -6x – 6x + 8 = 0 Put into standard form: ax 2 + bx + c then factor.

3) Let x = a number 2x 2x 2 2 + x = 6 -6 -6 + x – 6 = 0 4) Let x = a number 4x 2 – 7 = 18 4x 2 -18 -18 – 25 = 0 2) Let x = a number x 2 x 2 – 15 = 2x -2x -2x – 2x – 15 = 0 Put into standard form: ax 2 + bx + c then factor.

5) Let x =1 st CI x + 1 = 2 nd CI x(x + 1) = 56 x 2 + x = 56 x 2 -56 -56 + x – 56 = 0