missing constant

Question

what is the missing constant term in the perfect square that starts with x^2-8x

Answer 1

Hi Emma L.,

For your polynomial x² - 8x, a perfect square will need to look like (x - c)² as opposed to (x + c)² due to the minus sign (-8x). And (x - c)² = x² - 2cx + c², where c² is the missing constant. Lets compare the two equations:

x² - 2cx + c²

x² - 8x

The two middle term need to equal each other:

-2cx = -8x

c = 4, [remember this c is from (x - c)² to become (x - 4)², but we need c²]

c² = 16

Completing the square for your given polynomial:

x² - 8x + 16

You can also find the constant from (b/2a)², for a polynomial of the form ax² + bx + c.

Maybe you can try it that way to see what you like best.

I hope this helps, Joe.

Answer 2

the formula is (b/2)^2 = b^2/4

A=1 B=-8

(-8/2)^2 = (-4)^2 = 16

so the completion of the square is x^2 - 8x + 16 = (x -4)(x-4) = (x-4)^2

the answer is 16