Polynomial Expressions — Test

Question 2 • Algebra 1

How could Brent use a rectangle to model the factors of x squared minus 7 x plus 6 ?

Answer

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

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

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

He could draw a diagram of a rectangle with dimensions x plus 7 and x minus 1 and then show the area is equivalent to the sum of x squared , 7 x , negative x , and 6 .

Explanation

To factor x² − 7x + 6, find two numbers whose product is 6 and whose sum is −7: −1 and −6. So the factors are (x − 1)(x − 6). Multiplying the dimensions gives x² − 6x − x + 6, which matches the rectangle’s area and the original expression. Choice B gives these dimensions and area terms.

AI-written and checked against the verified answer.

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