Problem 1085

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then, write and factor the trinomial.

x² – 14x

 

Solution : –

 

If  x² + bx is a binomial, then by adding , which is the square of half the coefficient of x, a perfect square trinomial will result.

x + bx + = (x+

To complete the square, add the square of half the coefficient of x.

The coefficient of x is -14, so half the coefficient is – = -7.

The square of half the coefficient of x, -7x is (-7)² = 49.

To write the trinomial, add the constant 49 to the original expression. The resulting  perfect .

To write the trinomial, add the constant 49 to the original expression. The resulting perfect square trinomial is x² – 14x + 49.

Finally, factor the trinomial x² – 14x + 49.

x² -14x + 49  =  (x – 7)²