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AnnyKZ [126]
3 years ago
12

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

line{~~~~}.\]$
Mathematics
2 answers:
saw5 [17]3 years ago
8 0

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

<em />

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

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

mixas84 [53]3 years ago
3 0
The answer would be x^2+22x+121
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