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.

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.

Step-by-step explanation:

For the factors of this trinomial, we want factors of 6 that sum to -7.  The factors of 6 are:

1 and 6;

2 and 3;

-2 and -2;

-1 and -6.

The only pair that would sum to -7 is -1 and -6.  This makes the factors x-1 and x-6.

The area would then be equal to the sum of x(x) = x²; x(-6) = -6x; x(-1) = -1x; and -6(-1) = 6.

Step-by-step explanation:

Since Brent uses a rectangle that models the area = (x² - 7x + 6)

Now we will factorize this expression

x² - 7x + 6 = x² - 6x - x + 6

                = x(x - 6) - 1(x - 6)

                = (x - 1)(x - 6)

Therefore, (x -1) and (x - 6) will represent the sides of a rectangle so that multiplication of the sides will model the area of the rectangle.

the correct answer is C