Question

Fill in the blank with a constant, so that the resulting quadratic expression is the square of a binomial. $\[x^2 + 22x + \underline{~~~~}.\]$

Answer 1

Answer:

$\[x^2 + 22x + 121\]$

Step-by-step explanation:

Given

$\[x^2 + 22x + \underline{~~~~}.\]$

Required

Fill in the gap

Represent the blank with k

$\[x^2 + 22x + k\]$

Solving for k...

To do this, we start by getting the coefficient of x

Coefficient of x = 22

Divide the coefficient by 2

$Result = 22/2$

$Result = 11$

Take the square of this result, to give k

$k= 11^2$

$k= 121$

Substitute 121 for k

$\[x^2 + 22x + 121\]$

The expression can be factorized as follows;

$x^2 + 11x + 11x + 121$

$x(x + 11)+11(x+11)$

$(x+11)(x+11)$

$(x+11)^2$

Hence, the quadratic expression is $\[x^2 + 22x + 121\]$

Answer 2

The answer would be x^2+22x+121