Measures of Center

Question 3 • Common Core Algebra I B-IC

How could Brent use a rectangle to model the factors of x2 – 7x + 6?

Answer

He could draw a diagram of a rectangle with dimensions x – 3 and x – 4 and then show the area is equivalent to the sum of x2, –3x, –4x, and half of 12.

He could draw a diagram of a rectangle with dimensions x + 7 and x – 1 and then show the area is equivalent to the sum of x2, 7x, –x, and 6.

He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.

He could draw a diagram of a rectangle with dimensions x – 4 and x + 3 and then show the area is equivalent to the sum of x2, –4x, 3x, and half of –12.

Explanation

To factor x² − 7x + 6, find two numbers whose product is 6 and whose sum is −7: −1 and −6. Thus x² − 7x + 6 = (x − 1)(x − 6). A rectangle with those side lengths has partial areas x², −x, −6x, and 6, which add to the original expression. That matches choice C.

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