IM Alg1.7.6 Lesson: Rewriting Quadratic Expressions in Factored Form (Part 1)

Here are puzzles that involve side lengths and areas of rectangles. Can you find the missing area in Figure A? Be prepared to explain your reasoning.

Can you find the missing length in Figure B? Be prepared to explain your reasoning.

Use a diagram to show that each pair of expressions is equivalent.

[size=100]Observe the pairs of expressions that involve the product of two sums or two differences. [/size][br][br]How is each expression in factored form related to the equivalent expression in standard form?[br]

Each row in the table contains a pair of equivalent expressions. Complete the table with the missing expressions. If you get stuck, consider drawing a diagram.

[size=150]A mathematician threw a party. She told her guests, “I have a riddle for you. I have three daughters. The product of their ages is 72. The sum of their ages is the same as my house number. How old are my daughters?”[br][br]The guests went outside to look at the house number. They thought for a few minutes, and then said, “This riddle can’t be solved!”[br][br]The mathematician said, “Oh yes, I forgot to tell you the last clue. My youngest daughter prefers strawberry ice cream.”[/size][br][br]With this last clue, the guests could solve the riddle. How old are the mathematician’s daughters?

Information: IM Alg1.7.6 Lesson: Rewriting Quadratic Expressions in Factored Form (Part 1)