Chapter A.3, Problem 143AYU

To determine

To find: Make up a polynomial those factors into a perfect square.

Answer to Problem 143AYU

The sign of the first and second term in the squared binomial is always same as the sign of the middle term in the trinomial.

The first and last terms of a perfect square trinomial must be positive, because they are squares. For example, the polynomial $x^2-2x-1$ cannot be a perfect square, because the last term is negative.

Perfect square trinomial can also be factored by using grouping or FOIL method, although using the method of this section is often easier.

Explanation of Solution

The sign of the first and second term in the squared binomial is always same as the sign of the middle term in the trinomial.

The first and last terms of a perfect square trinomial must be positive, because they are squares. For example, the polynomial $x^2-2x-1$ cannot be a perfect square, because the last term is negative.

Perfect square trinomial can also be factored by using grouping or FOIL method, although using the method of this section is often easier.