Do you know what the FACTORS are of this generic rectangle

The two factors are x+7 and x+2

The polynomial factors to (x+7)(x+2)

Explanation:

In the upper left corner we have x^2. We get this by multiplying x with x

So,

x*x = x^2

This means you'll have x to the left of x^2, and another copy of x above the x^2. These new terms are outside the box.

Now ask yourself, what goes in the blank x times ___ = 7x. The answer must be "7" since x times 7 = 7x. So we'll write 7 above the 7x, outside the box. Up top, the x and 7 help form the factor (x+7)

Along the left side, the other factor is (x+2) for similar reasoning. Notice how we effectively have x times ___ = 2x and '2' must go in the blank. So a '2' must go to the left of the 2x.

Putting everything together, the two factors are (x+7) and (x+2).

Therefore, x^2+7x+2x+14 fully factors to (x+7)(x+2)

This is the same as saying x^2+9x+14 factors to (x+7)(x+2)

The order of multiplication doesn't matter.

(x-4)^2 + 6

Step-by-step explanation:

(x-a)^2 + b = x^2 - 2xa + a^2 + b

x^2 -2xa +a^2 + 6 = x^2 -8x +22

Hence:

-2xa = -8xa

a^2 + b = 22

b = 22 - a^2

b = 22 - 16

b = 6