Question

Complete the square for the expression. Then factor the trinomial.t²-22t.

a) (t-11)²
b) (t-22)²
c) (t-11)(t-22)
d) t²-44t

Answer 1

To complete the square for the expression t² - 22t, add 121 to form the perfect square trinomial t² - 22t + 121, which factors to (t-11)². The correct option is a) (t-11)².

Step-by-step explanation:

To complete the square for the quadratic expression t² - 22t, you need to find a number that, when added to this expression, forms a perfect square trinomial, which can then be factored into the square of a binomial.

First, we determine the number to add by taking half of the coefficient of t (which is -22) and squaring it:
(-22 / 2)² = (-11)² = 121.

Adding 121 to the expression t² - 22t gives us a perfect square trinomial:
t² - 22t + 121.

Now, the expression can be factored as the square of a binomial:
(t - 11)².

Thus, when completing the square for the expression t² - 22t, the correct option is a) (t-11)².