Find the missing term in a perfect square trinomial calculator

SolutionHelp

1. Completing the square for quadratic equation

$3x^2+5x+2$

$9x^2+6x+1$

$x^2+6x+9$

2. Determining if the polynomial is a perfect square

$4x^2 + 4x + 4$

$x^2 - 4xy + 4y^2$

$30xy - 25x^2y^2 + 9$

3. Find the missing term in a perfect square trinomial

$x^2$ + ____ + 4

$9x^2$ - ____ + 16

3. ____ +

$12x^2$ + 9

$49x^2$ + 56 xy + ____

$25x^2$ - ____ +

$121y^2$

$9x^2$ + ____ +

$y^2$

$x^4y^2$ -

$10x^2yz$ + ____

Example

1. Find Missing Middle Term of a given equation $x^2+4$

Solution:

$x^2+4$

Here

$"F.T. = x^2, L.T. = 4 and M.T. = ?$

$(M.T.)^2 = 4(F.T.)(L.T.)$

$:. (M.T.)^2 = 4 * x^2 * 4=16x^2$

$:. M.T. = 4x$

So polynomial is

$x^2+4x+4$

2. Find Missing Last Term of a given equation $x^2+6x$

Solution:

$x^2+6x$

Here

$"F.T.=x^2, M.T. = 6x and L.T. = ?$

$(M.T.)^2 = 4(F.T.)(L.T.)$

$:. L.T. = (M.T.)^2 / (4(F.T.))$

$= (6x)^2 / (4 * x^2)$

$= (6x * 6x) / (4 * x^2)$

$= 9$

$:. L.T.=9$

So polynomial is

$x^2+6x+9$

3. Find Missing First Term of a given equation $6x+1$

Solution:

$6x+1$

Here

$"L.T.=1, M.T. = 6x and F.T. = ?$

$(M.T.)^2 = 4(F.T.)(L.T.)$

$:. F.T. = (M.T.)^2 / (4(L.T.))$

$= (6x)^2 / (4 * 1)$

$= (6x * 6x) / (4 * 1)$

$= 9x^2$

$:. F.T.=9x^2$

So polynomial is

$9x^2+6x+1$