Find the constant term that should be added to make the following expression a perfect square trinomial.
x^2-2x
x^2+3x
Take one half the second term, square it.
1/2 *2=`1, squred, 1
1/2 *3=3/2, squared, 9/4
To make a quadratic expression a perfect square trinomial, you need to find the constant term that should be added.
For the expression x^2 - 2x, take half of the coefficient of the x term, which is -2. Half of -2 is -1. Square this value: (-1)^2 = 1. Therefore, adding 1 to the expression will make it a perfect square trinomial: x^2 - 2x + 1.
For the expression x^2 + 3x, take half of the coefficient of the x term, which is 3. Half of 3 is 3/2. Square this value: (3/2)^2 = 9/4. Therefore, adding 9/4 to the expression will make it a perfect square trinomial: x^2 + 3x + 9/4.
To make the expression x^2-2x a perfect square trinomial, you need to add the square of half the coefficient of the x-term. The coefficient of the x-term is -2, so half of that is -1. Squaring -1 gives us 1.
Therefore, the constant term that should be added to make the expression x^2-2x a perfect square trinomial is 1.
To make the expression x^2+3x a perfect square trinomial, you need to add the square of half the coefficient of the x-term. The coefficient of the x-term is 3, so half of that is 3/2. Squaring 3/2 gives us 9/4.
Therefore, the constant term that should be added to make the expression x^2+3x a perfect square trinomial is 9/4.