Question

how could brent use a rectangle to model the factors of x² - 7x + 6? 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:

Step1: Factor the quadratic

Factor \(x^{2}-7x + 6\) to \((x - 1)(x - 6)\) using \(x^{2}+(a + b)x+ab=(x + a)(x + b)\) where \(a=-1,b = - 6\) and \(a + b=-7,ab = 6\).

Step2: Check rectangle - area

The area of a rectangle with sides \(x - 1\) and \(x - 6\) is \((x - 1)(x - 6)=x^{2}-6x - x+6=x^{2}-7x + 6\).

Answer:

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 \(x^{2},-x,-6x\), and \(6\).